They're easy for a beginner in the sense that UI-wise they can be done in a pretty simple way, you don't even have a timer to cope with (actions aren't in real time, it's entirely turn-based). The AI is a completely different situation, though you can always avert that by forcing only humans to play =P The rules of board games are also complex, but at least they're very well defined (they need to be interpreted by humans, after all!) so ultimately they're more of a time sink than actually being hard to implement. You don't even need to do it in a very optimal way given it's all turn based (no framerate to worry about).
For AI on board games the most common trick is to assign points to each possible thing that can happen, then try all possible moves and see which one has the best score (then do that). To make the AI harder you can try several turns ahead, but then the computation time can explode exponentially so maybe as a beginner you may want to avoid considering that one.
Tic-Tac-Toe has so few possible combinations you can just brute-force the way through it...
EDIT: by the way, there's an old DOS game called Tetris Deluxe that does exactly the same thing as I mentioned for board games. Even when you take into account the next piece it amounts to a total of 81 possible moves, and the "AI" can end up doing some surprisingly smart moves a human player would initially consider stupid. So yeah, that method works on Tetris too. It's pretty fast, consider that game was made on a 4.77MHz 8088 =P