Step 1: Tree Sources
First, go out to your backyard. Find a tree that your cruel, heartless parent (lol) is about to pull and offer to replant it. That's what I did. Or go to a field or other generally well-tended boring grassy place and rescue a tree from there.
Remember, don't ever take a tree from somewhere it will be happy. It will be fine there. Go find one in danger.
BUT DON'T PULL IT YET.
Step 2: Rescuing a Tree
Find your tree, and estimate the size of its root ball. Then using your shovel, draw a circle about 200% bigger in the ground around it. Dig all the area in this circle up, trying to keep it in on piece as to not hurt the root ball.
Then pick up your tree from the strongest part (probably supporting the bottom of the roots and the bottom of the "trunk", and brush as much dirt and bugs as possible off the roots. Then plonk it lightly in your pot and put the soil you brought in. Water the tree, pat the dirt you dug up back into the hole, and leave with your new friend.
Step 3: Getting a Home.
So go out to your local garden center/borrow from that understanding human in step 1, etc. Just get a pot about 4 times bigger than his root ball. Don't put him in the ground. He might survive, but the shock for the young tree of being transplanted and having to fight off all the inherent dangers of being in the wild may be too much.
Also get some more soil, preferably planting or potting soil. Miracle Grow works great for my needs.
Finally, a little fertilizer cant hurt. Make sure you get the right type, just read what its for. you will probably want something that says 'sapling", "baby plant", "Potting", etc. However, something labeled "flowering" or 'flowers" is common but not what you want.
First, fill the pot about 3/4 of the way up with some of the soil. Using your hand, dig a small hole in the soil and place the tree right way up in the pot. Then continue filling the pot until the soil reaches the bottom of the "trunk". Now fertilize with a light sprinkle and water profusely.
Step 4: Getting a Home for the Home.
1. You wont forget about it so you remember to water and occasionally fertilize it
2. There's plenty of sunlight
3. There's plenty of room
4. There's no pets/ small children to devour/kill/knock over the tree.
How? First, pick if you want it inside or outside. With inside comes the promise of protection from bugs, heat, cold, thunderstorms, alien invasion, etc. But it comes with the burden of small children, pets, and the dreadful cycle of drought and flooding as you forget to water it and then fill it to the brim with water. Outside there rain, but its vulnerable to other things like bugs, heat, etc.
What do I do? I keep mine next to the kitchen sink. No small children or pets in my house though, so being next to the kitchen sink allows me to easily water any plants I'm saving.
Chose a place? Good. Now, on to the next step....
Step 5: Getting to Know Your Tree
The tree's species gives you a wealth of information. You now know what diseases its susceptible to, what soil it likes best, the climate its good in, what bugs it might harbor, etc.
Step 6: Watering and Fertilizing Schedules
Watering: Pretty variable, but a good rule of thumb is this. If the surface is dry or its been awhile since watering, stick your finger down about an inch. If no or very little amounts of dirt stick to your finger, don't water, or water lightly. You can also sometimes buy/make trays that go under your pot. You fill them with water and the tree sucks it up through the hole on the bottom of the pot.
Fertilizing: This is even more tricky. There should be instructions on the container, but if in doubt, no more than about once every 2 months, and only a light sprinkle.
Step 7: It GROWS
As the tree grows, you will find that you may need to switch pots. Don't let the pot get too small, but don't be switching your tree out constantly either. That can kill it. Usually, its better to err on the side of caution and not transplant it quite yet.
When moving a tree from pot to pot, simply tap and shake the pot to free the root ball, tilt the pot downwards, and grabbing the edges of the dirt-clump that comes out, gently slide the tree out. Then (not taking any dirt off), dig a hole big enough in the new pot to fit the incoming tree and place in. Cover the roots with dirt, water, and fertilize if you haven't for a while.
(Yes, I know that the pictures aren't of a tree, but its exactly the same and all I had)
Step 8: When Its Almost Ready.
Also, the right time of year. Spring is good, because it will be warm and your tree will have a while to grow before the cruel winter months. A few weeks after the last frost is good.
Step 9: Letting It Go Into the Wild.
If you own land, that's a good spot. Just find a nice looking place, dig a hole in a similar manner that you planted him in the pot (water and fertilizer too!) , say goodbye, and you're done. Be sure to check every few days for a few months to make sure the tree is doing OK.
If you don't, you have a small problem. See if any friends or relatives want to plant him on THEIR land. Contact your local government about planting it on a street median or an unused field. Try Guerrilla Gardening. Try anything.