First, just in case you didn't know, this should be your most important link (use the 2010 pages mainly):
http://df.magmawiki.com/index.php/Main_PageThere are two types of plants - above ground and underground.
You typically embark with seeds for underground ones, but you can get above-ground ones by harvesting random bushes if they grow naturally where you are, or from trading.
In either case, they can only be planted in soil (sand counts as soil; rock/stone do not).
The underground ones have to be planted in mud - this requires your soil to have been wet. So typically people will somehow get some water onto those soil tiles, and then let it evaporate (there are 7 depth levels to water, but you want to stop adding water at level 1 so it evaporates).
Pumps are one way (see the wiki on how to build a pump STACK) - pumps themselves are BUILDINGS so you don't need a mechanic or a mechanic's workshop for them.
If you have the components, then you set a place for the pump in the build ('b') menu. Then you need an architect, who will come and do some building-designer stuff, and then you need a carpenter/metalsmith/mason, depending on what materials the pump is made from, who will finish the job.
But it may be easier to just path water to your farm (like from a river or pool), build a door with a lever in between, and then close the door with the lever when there's enough water to make the mud. It's usually quicker than pumps although it could expose your fortress to the outside and other things.