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I had a DNA test done with Family Tree DNA while searching for my birth parents. I have identified 2 half-sisters on my birth father's side and several cousins on my birth mother's side. The closest one matches 206 cM with the longest block being 68. Family Tree says he is a 2nd or 3rd cousin.
How do I know which one he is?
Since we know the connection is on my birth mother's side, would I be looking for grandparents on his mother or father's side or great-grandparents?
Knowing that two people share a certain amount of DNA is in general not enough information to determine the exact relationship. That's because there is a significant amount of randomness in how much DNA is shared by say second cousins, or second cousins once removed, or third cousins, etc. The Shared Centimorgan Project has compiled statistics about how many centimorgans are shared by people with various amounts of DNA, based on reports submitted to them for pairs of people with known relationships.
If you go to this Shared cM page, you can enter the number of shared centimorgans and see which relationships are most likely.
For 206 cM, it says there's a 47% chance the relationship is one of "Half GG-Aunt / Uncle 2C Half 1C1R 1C2R Half GG-Niece / Nephew", 43% chance the relationship is one of "Half 2C 2C1R Half 1C2R 1C3R", and 6% chance the relationship is one of "Half 1C3R † 3C Half 2C1R 2C2R".
At this point, you will likely have to start using other sources of data to try to figure out the exact relationship. Either DNA matches with other people, or written records, or both. Good luck!
