Hypothetical: effects of multiple moons on the planet?

Oh, my brilliant, genius Jellies! So many of you have knowledge far beyond mine.

I write stories from time to time, and I’ve been developing this fantasy planet since I was 14 or so, and I’ve never taken into account the moons. Originally there were three, but I’m cutting it down to two (the mythology has had a recent upheaval. ^_^).

Okay, so assuming that everything else is equal to Earth, what would be the effect of having a second moon? One about half the size of Luna, with an opposite orbit (i.e., when Luna is over the Eastern hemisphere, mini-moon is over the Western)? I’m assuming the tides, at least, would be affected, but how?

We don’t need to get too terribly technical, but if we’d all fly off into outer space, that’d be good to know, too. ^_^