If the edges of your table are relatively thin, then clothes pegs are almost the perfect option for holding down outdoor tablecloths, as they're readily available and do an excellent job of securing your tablecloth.
The only drawback is that they may not exactly be the most attractive option. However, who is really going to notice or care? If anyone notices them, their first thought will probably be "hey, that's quite clever, why haven't I ever thought of that?".
Most people have multicolored sets of pegs, meaning you can choose colors which blend in with your cloth. You may even be able to do this in a way where you secure the cloth, and allow for more of the tablecloth to hang down over the peg, preventing it from being visible.
If you have thicker edges which will be too wide for a peg to clamp on to, read my blog post on specialized table edge clamps.