Hydroelectric power is, generally, generated using the potential energy of dammed water and converting it, by driving a turbine and generator, into electrical energy. This can be artifically created by releasing water from a high reservoir to a lower one, a technique usually used to handle increased demand. (Tidal and other methods I'll cover later.)
Hydroelectric plants have absolutely no fuel cost. They also tend to last longer and have few regular on-site personnel, thus decreasing operating costs. Dams are also relatively low-cost, if the dams also serve other purposes that can generate revenue (e.g., reservoirs can be used for water sports, fish farming, irrigation, and flood control). However, there are strict limits on how many sites are appropriate for dam construction; and, since many sites are some distance from population centres, hydroelectric plants will require more transmission infrastructure than other technologies.
The most significant problem with building a hydroelectric plant is the potential for damage to ecosystems. Both upriver and downriver environments can be altered, affecting wildlife in a variety of ways. For example, turbine activity alters the speed and temperature of water flow, and oxygen levels can be changed from pre-dam levels. Furthermore, the failure of a dam can be disastrous. So, there is a long lead-time before a dam can be constructed, due to the need to carefully assess the potential a given area has for successful (and minimal impact) dam construction.
In terms of output costs, while dams themselves produce no emissions, the reservoirs can, if they contain plant material which then decomposes. This decomposition can release large quantities of methane, a greenhouse gas.
The generating capacity of a hydroelectric plant varies widely with the size of the dam. Suffice to say, though, given the limited potential development, hydro plants reliant on large dams are, at best, only a part of the long-term solution to power needs. Even if we factor in the possibility of small dams, there's still an upper limit to how many dams can be constructed -- and how much damage can be done to aquatic ecosystems -- before the cost of generating more power outweighs the benefit of the electricity gained.
Nuclear reactors work in almost the same way as fossil fuel plants. That is, heat is produced to boil water, which becomes steam, which drives a turbine, which turns a generator. The difference, of course, is that the fuel isn't burned; instead, a controlled chain reaction is used to generate the necessary heat. The fuel is a form of uranium, possibly enriched to have its uranium-235 (U-235) content increased above what is found in nature. As far as I can tell, all current commercial power-generating reactors use a moderating material of some kind to slow the neutrons emitted by U-235 as it decays. Slowing the neutrons increases the probability they will fission particles of U-235, and reduces the probability they will be captured by U-238.
There are a number of different reactor types in use. Most American reactors are cooled and moderated by high-pressure liquid water. Some use lower-pressure water, which can be allowed to boil (increasing efficiency, but also increasing stress on reactor components). The CANDU reactors (Canadian-designed) are cooled and moderated by high-pressure heavy water. RBMK reactors, a Soviet design, are water-cooled and use graphite as a moderator, but are considered unstable and highly dangerous. Gas-cooled reactors, originally developed in the UK, are graphite-moderated and cooled by CO2. Reactors cooled by liquid sodium operate by slightly different principles. They are entirely unmoderated and thus the probability of fission is lower. It's hard to see where the technology will go, so I'll try to speak of the costs and benefits of all reactors in general (allowing that this probably obliterates some distinctions). I think I can get away with this because the economic differences between reactor types -- for example, CANDU does not require enriched uranium -- can be oblitered by differences in the other direciton -- CANDU requires tonnes of nearly pure heavy water.
Generally speaking, the economic costs of nuclear plants are heavily-weighted towards construction. Maintenance and fuel are minimal by comparison. It's generally taken as gospel by anti-nuclear types that nuclear technology is too expensive; they like to point to the cost overruns associated with refurbishing Ontario plants, such as in Darlington. Whether or not nuclear is too expensive really depends on how much power we can expect nuclear plants to generate; however, it seems to me that the cost overruns in Ontario aren't entirely due to the technology itself. It's worth noting that CANDU reactors installed in other parts of the world managed to come in on-schedule and on-budget.
Construction cost estimates run from $1000 to $3000 per kilowatt-electric (i.e., per kilowatt of electric capacity). Fuel costs in 2007 are about $250/kg, and rising. Nuclear plants must also invest more in security than other generating technologies, given the possibility of sabotage or theft of nuclear material. And, nuclear plants are subject to stricter regulations, which also increases operating costs. Costs associated with mining uranium must also be factored into the input costs of nuclear reactors, as well as the fact that uranium supplies worldwide are limited, just as are fossil fuels. While it may be possible to use materials other than naturally-occurring U-235, there will still, inevitably, be a point beyond which there is no more fuel. (Pie-in-the-sky predictions about the longevity of nuclear fuel supplies sound, to me, like the promises made of fossil fuel supplies in the last-but-one century.)
As far as output costs, waste is a bit of a bugbear. Strictly, nuclear waste doesn't all have to be stored; it can be reprocessed for additional fuel, and for weapons material. While it's not perfect, it does suggest that fears of waste disposal may be exaggerated (to put it mildly). Furthermore, the amount of waste produced by nuclear plants is far less than the total amount of toxic industrial wastes from all industries; and burning coal releases even more radioactive waste. Radiation, generally, is a bugbear, as there is no evidence to support the claim that proximity to a nuclear plant increases one's chances of developing any kind of illness or injury. Nuclear plants also produce no airborne emissions: no greenhouse gases or any other pollutants. Reactors largely emit water vapour.
I'd be remiss if I didn't say something about Three Mile Island and Chernobyl, so: Three Mile Island is highly exaggerated, and Chernobyl is likely a one-time problem. Three Mile Island released very little radiation, much less than natural background radiation; there are also no confirmed injuries, fatalities or illnesses sustained as a result of the Three Mile Island accident. Chernobyl, by contrast, did kill thousands, and will probably go on to kill thousands more. However, the reactor designs were clearly flawed and have been significantly improved. (It'd be interesting to see if, and to what extent, there were accidents with early fossil fuel plants.)
In terms of cost per kWh, Wikipedia cites an MIT study which concluded the cost to be 6.7¢ per kWh; a US government 2006 study, assuming $1984 per kWe in construction (and related) costs, concluded nuclear power costs approximately 6¢ per kWh. Given that nuclear power is, ultimately, just a refined version of the technology used for fossil fuel plants, it strikes me that, as fossil fuels were a time-limited improvement on burning wood, nuclear power is not a long-term solution to power needs. This does not mean, though, that it'd be a good idea to not build any nuclear plants. After all, they're still, fairly obviously, better than fossil fuel plants. The question is whether they're better than the other contenders.
Generally, electricity is generated from wind power by converting the rotation of the blades of a wind turbine (kinetic energy) into electrical energy via a generator. Simple enough. Wind turbines will not, however, work in environments that routinely experience heavy wind gusts or temperatures of less than -20°C. Wind turbines can either be large-scale, and contained in large wind farms, or small, which can be attached to individual buildings to provide small amounts of electricity.
As far as input costs go, wind power requires no fuel. Installation costs in the US are around $1600/kW. As with hydro, most good sites for wind turbines are far from population centres, increasing the cost of transmission infrastructure; nonurban and offshore locations are probably best, in terms of reliable and usable wind, but will be most costly in terms of transmission needs.
The use of internal heaters, low-temperature lubricants, and the like can, in theory, allow turbines to operate in low-temperature conditions. However, this increases the operating costs of the turbine, as (for example) power is required, in some form, to operate the heaters.
In terms of output costs, wind power produces no emissions. Unlike hydro, it's not yet settled what effects, if any, large-scale wind farms have on surrounding ecosystems. It's probable that some species will be at risk, as with any other human activity, and we should try to minimize that cost. Certainly many people find them unsightly, but I'm confident many people also don't care one way or the other. The issue of noise pollution is exaggerated, as wind turbines produce sound levels comparable to a mild wind.
The cost of the electricity generated by wind turbines in 2006 was approximately 6&162; per kWh.
Albert Betz, according to Wikipedia, determined that a wind turbine can extract at most 59% of the energy that would otherwise flow through the turbine's cross section, as the air is slowed down by passing through the turbine. Due to the variable nature of windspeed, the amount of power generated by wind turbines will vary. The ratio of actual productivity in a year to the theoretical maximum capacity (the capacity factor) is about 30% for a well-sited wind turbine. This could be improved, in principle, by scattering wind farms in different climate regions, but it's probably impossible to have a perfectly stable energy supply based on wind power. Even energy storage solutions -- which, it must be noted, would increase the cost of wind power -- can only improve, but not resolve, the situation. Wind power is also plagued by the problem of the intermittency of the wind, and of the practical limit on the number of locations where wind farms can be placed before environmental impact becomes too great to be tolerated. As with hydro, it seems that wind can, at best, be a part of a long-term energy solution.