There are several types of hydroelectric systems, each which is best for a very specific set of circumstances.

For really high pressure but low flow, a Pelton wheel turbine is usually used.

For lower pressure and more flow, a Turgo wheel turbine is ideal.

For low pressure, like 5-10 feet of head, but good flow, a shrouded blade design is best.

For really low pressure but gobs of flow (like a slowly flowing river) an unshrouded blade or darrieus turbine is best. (imagine a small wind turbine, but underwater)

Fortunately there are companies out there that can provide you with whatever you need. I really like PowerSpout turbines (although the have to be imported), because the generators can be modified to suit your flow and head perfectly. Their website is

http://powerspout.com/.

You don't necessarily need a dam, but a weir and intake is needed.

Now, to estimate how much flow and head you have.

First, measure more accurately how much river length you have. Then, throw a float in the upstream and time how long it takes to get to the downstream end.

Now, measure the average width and depth of the river. Multiply these together and divide by 2 (this is assuming that the flow profile of the river is triangular, a conservative estimate)

Now convert these numbers into flow. Example:

a river 10 feet wide and 4 feet deep, 1000 feet long. It takes 3 minutes for the float to travel the 1000 feet.

Volume = 10 x 4 / 2 x 1000 = 20,000 cubic feet of water.

Flow rate = volume/time = 20,000 square feet / 3 minutes = 6,667 cubic feet per minute.

One cubic foot is 7.5 gallons. So you have 50,000 gallons per minute.

Next you will need a level. From the upstream side, find a level. Now have a friend go to the downstream end and hold a stick up until you can sight down the level and see the end of the stick. Measure that height. You may need to do this several times to get the total drop.

This will be your head. Say it's 50 feet over 1000 feet.

Now pop these into the PowerSpout calculator. When I did, it told me:

"At your location, 16 PowerSpout(s) could each generate up to 423 Watts for a total of: 6768 Watts"

Now you need to figure out a real-world solution. You are not likely going to use more than one turbine, so you could get 423 Watts from just one. Based on that, you are only going to need to divert 1/16th of the flow of the river to power it. However, it is probably impossible for you to build a sluiceway 1000 feet long. Say you can do 100 feet. Well, you will want to choose the 100 feet of your river with the most slope. Say that's 12 feet of drop over that distance. Now the calculator says each turbine can produce 114 Watts.

That sounds doable. 114 Watts is 2.7 kWH per day or almost a megaWatt-hour per year. That's enough power for 25% of an efficient home or all of a super-efficient home. If it turns out the sluiceway is the most expensive part, then install more turbines to offset more power. There is plenty of flow for it (at least in this example)