Many abilities deal damage based on your current DPS, but the problem is I don't know how much my DPS is. In the character's menu your current damage is shown, but to compute DPS I need more data like total attack rate (which I also couldn't find). Do I have to just guess my total DPS or is it written somewhere?
If you press J to bring up the Arcane Statistics panel, you can see all kinds of useful, and detailed information about your character.
It contains information on things like your resistances, your hit chance, your calculated damage per hit (not sure about actual 'DPS'), attack speed, your regeneration speeds, various percentages, and lots more that I can't remember right now. If your DPS is listed anywhere in the game, this is where it will be. If it isn't, the information you need to calculate it definitely is.
Extra Info About Attack Speed
If you're just looking for base attack speed, that's usually listed in seconds when you hover over your weapon.