Rubber farming is fairly easy, because the hardest part is simply finding a tree or two to start with.
Step 1: Find those rubbery leafed buggers.
Rubber trees are characterised by the two or three leaf blocks sprouting from the top (easily visible in the image) and their dark wood. They are easy to spot from a distance, but if you're having trouble finding any, Swamp biomes tend to have a large amount of Rubber trees. Their leaves are transparent, even if your graphics are set to 'fast', so this can be an easy way to identify them.
Step 2: Get saplings. Go to your rubbery friends and remove their leaves untill you have a few of their saplings. Then chop them down. Rubber wood equals three planks (until you get an extractor, where you can convert it into one rubber). The rubber logs also have a 15% or so chance of releasing a sticky resin themselves.
Step 3: Make a walled enclosure for your rubber trees (you can skip this too, but it's a recommended step if you don't want creepers "inspecting" your progress).
Step 4: Plant Rubber Trees and wait for them to grow. For convenience and ease of harvesting, place them four or five blocks apart in a regular grid.
Step 5: Make a Treetap using 5 pieces of wood on a crafting bench.
Step 6: Farm the hell out of those Rubber Trees.
Find an amber rectangle on a Rubber Tree's trunk and, while holding the Treetap, right click that section of trunk. 1-3 pieces of rubber will then pop out of the tree. If you use the treetap on that section where the amber section was on there, you could get more rubber, but the resin hole (that's what i call it) may dissappear and not spawn any more resin.
Congratulations, you've sucessfully farmed your first piece of Rubber!
The rubber on the trees respawns after 2-3 ingame days, and when you have machines like the Extractor, you can obtain much more Rubber from a Rubber Tree than usual if you don't wish to chop the trees down. However, it takes much more time to wait for the rubber to respawn than it takes to simply grow new trees and expand your farm.