This is one of the most rewarding ways of acquiring a bonsai. You must however get the site owner’s permission. Sources of this type of material are:
Garden clearance, Building sites/new road works, or perhaps your local farms. Keep your eyes open and explainto the site owner what you want to do.

Don't be put off by larger bits of material, particularly deciduous trees; these will bud back from the trunk. These buds will allow you to develop a new head and branches. Trees with 6-10cm wide trunks will make good bonsai.

A newly collected stump (as picture on the right) and how it could look in a few years. The trunk had been hollowed out to give the impression of taper. This technique is called Sabamiki.
If at all possible try to spread the collection over two years. The first year dig a trench around the tree, severing any major roots. Treat these cut ends with rooting powder and fill the trench in again. This will form new fiberous roots close to the trunk and aid the trees survival when you come back to collect it. Year two dig the trench out carefully and avoid too much rooting damage.

Or

You can dig the tree out without waiting a year, cut all big roots, trying to avoid removing to much soil from the root ball, as this will stress the tree. Wrap the root ball in a cloth or bag and tie it up. If you are going to lift the tree at the first attempt, cut under the tree with a spade and saw through any roots, then ease the root ball into a bag.

Remove all thin branches and all leaves; only leave the main branches you want to use.
Before collecting you should have a container large enough to cope with the tree, I use plastic washing bowls with large holes cut in the bottom. You should also have fairly gritty compost available.

For wild olives and white olives we have had 100% success rate by doing the following.

1. Remove all branches just leaving main branches.
2. Remove all foliage.
3. Plant the tree in a big container with a mix of 50% compost and 50% washed out river sand.
4. Place the tree in direct sun light and water in the morning and in the afternoon.
5. After you have planted the tree create a liquid mixture of a packed of backing yeast and one dispren (headache tablet) in two letters of low water. Give this to mixture to your tree after you have given the tree water for the first time. (I had a tree butting with in 14days after the above process was followed)

Don't be into much of a hurry to work on the tree, leave it for at least a year to recover.

Acknowledgment to Bonsai Primer.com

Bonsai, collecting trees for bonsai from the wild, Yamadori Bonsai