(Note: the old Forestry wiki was the source copied into this wiki and claimed Peat development only to a 1 block radius of water, and the new Forestry wiki doesn't even address manual Peat farming outside of machine farms (Peat Bog) and harvester devices (Turbary) mentioned below. So somewhere in there, the radius from water that Peat would mature went up. Upshot is, you can now manually farm Peat with more productive surface and fewer water blocks. This was observed and screenshots taken in FTB Ultimate (v1.0.1) which has Forestry 22.214.171.124)
Breaking mature Peat give you Peat and Dirt. Testing with Steel Shovel, Axe, Pick and Hoe seems to indicate that none of these tools is any faster than the others for manually digging Peat up (in non-machine harvesting.) In fact, your Fist or a block of Bog Earth manually digs Peat up at the same speed, so you may as well save tool durability. (If there is some special non-machine Peat-digging tool, please indicate in the Comments.)
A peat farm can also be built and maintained automatically by a Peat Bog, while a Turbary takes care of harvesting. Peat is used as solid fuel in peat-fired engines, providing 1 MJ/t for 5000 ticks. It's combustion in such an engine produces Ash at a rate of one per 1.5 peat, which can then be used to craft Fertilizer, Manure, or Bituminous Peat . Peat will burn very slowly. A single Peat Bog should produce enough fuel to keep as many as 10 peat-fired engines running.
Apart from fueling peat-fired engines, peat can also be used as a substitute in furnaces smelting 10 items each. It is to be noted that, despite peat being a lesser engine fuel than bituminous peat, the latter can't be used as furnace fuel. Also note that, when used as furnace fuel, no ash is produced.