Many 3D wooden puzzles are solved by putting them together after they are taken apart. These puzzles connect loosely and come apart with a little prying. Solving the puzzle is a matter of fitting all the pieces back into their original positions. If you can take notes on the process from disassembly to completion, it will help immensely in reassembling the puzzle.
Write down the steps you took to take the puzzle apart. Repeat those steps in the reverse when putting the puzzle back together again. This is the best method for putting a puzzle back together. Unfortunately, not everyone remembers to write down their puzzle disassembly process in the heat of the moment. Try taking notes on every step you take from this point on. You may also want to label the puzzle pieces alphabetically. You can also follow the reverse of the puzzle solution, if you have it.
Look at picture of the puzzle as it should appear when completely assembled. This will provide some assistance in reverse engineering your puzzle. Some puzzles like the wooden ball puzzle are meant to be solved in the reverse, so this is the puzzle. Examine each piece carefully to determine it's purpose and possible placement. If the pieces are all exactly the same, they will most likely connect to each other in a repetitive interlocking pattern.
Look up the solution to the puzzle. This simple method will ensure that you correctly put the puzzle back together again. This is a last resort for puzzle solvers who just can't figure it out. Put it off until you've tried every means possible at least. A puzzle is only intriguing as long as you don't know the solution.
Label the puzzle pieces numerically or alphabetically to help you keep track of them. Use a pen and paper to take notes on your puzzle solving process.