Do it well and thoroughly. It is more efficient and in the end more beneficial to send appropriate requests to fewer organizations than to send a shower of appeals in the hopes that one may land in the right place. While you may not receive an approval or even a hearing on the first attempt, if the appeal has been well thought out and is indeed within the guidelines of the foundation, the impression left is a positive one and the next time you try you may be more successful. Obviously, there are no guarantees, and since there are always many more appeals than resources to fill the need, a majority are turned down. Once you have determined that you are sending your appeal to an interested party, make sure that the form of your approach is correct.
Many foundations prefer a phone call or a letter of inquiry as the first step.
Others want a full proposal with all the required documentation. The letter should be addressed to an appropriate person. If for some reason in doing your research you are unable to find a contact name, call and ask. Again, if you have researched the foundation thoroughly, you will know what is required. However, you may have a heavy emphasis on preparing teachers, or computer programmers.