First you connect your M-Audio soundcard to your PC via USB, and the monitors to the soundcard's "out"s. Take the time to set up everything properly so that your computer does recognize the soundcard as your primary sound device, else the rest just won't work... Then you can either plug the mic directly to the soundcard (if it has phantom power) or to the mixer, then plug the mixer's "out"s to the soundcard's "in"s (it is likely that you will get better results with the mixer but if the MobilePre features phantom power you can try both solutions just to see... well, hear ;) which combination provides the result which suits you best).
Also, from your question I suppose that you don't yet have the cables, do you? so PLEASE, DON'T go for the cheapest cables as there IS a REAL quality difference between a 5$/5€ cable and a 15€/$ one. Of course you don't need 150€ cables for recording in a home studio, but the cheapest ones available on the market will totally "narrow" your sound, you will lose a lot of clarity in the signal and may get really disappointed by the result -- not because of your mic or soundcard, but just because of the cables...
In theory you could rely on your PC's internal soundcard, but it's definitely not advisable as the quality will most likely be very poor (you can try it anyway using a Y cable linking your mixer to the computer's line in plug)... In that case you most likely will need an ASIO driver if you want to record with an acceptable lag, try Asio4all (it works even with the cheapest internal sound cards). Unless of course if the mixer can also work as a sound card, but it doesn't seem to be the case of this model.
As for plugging the monitors to the mixer, it would provide you with the sound that you are recording, not that which comes out of the computer, which may be very different (especially if you want to sing over a playback, or if you want to apply effects to your voice such as a virtual reverb or something like that). Once again if your mixer wasn't designed to work as a sound card too then you definitely will need to rely on one. If you want to work with the internal sound card of your computer then you also will have to plug your monitors instead of your PC speakers.