Compression - now that's a kettle of fish :)

First - a good read http://www.barryrudolph.com/mix/comp.html understand what a compressor is and is used for. Not all audio need compressing, depending on the end result required, riding the volume (essentially what a compressor is doing for you) on the dialogue track yields far less artifacts (pumping, clipped fronts of words and background noise) and more pleasant results and should be the first port of call before you roll out the track slammer :)

Compressors used correctly can help, but also can butcher dialogue if thrown on without a bit of planning. Best thing to do is experiment with your DAWS compressor(s) and A/B the dialogue regularly to make sure it's not becoming flatter than a flat thing, leaving a bit of dynamic in the voice and gently squeezing can add density without pumping.

Lots of videos in youtube e.g.

Multiband compression is another story!

I'd skip the normalising as that will rob you instantly of headroom and save that (if using it at all!) until the end when you have levelled out the elements in the mix.

@soundgh2 This is a really nice explanation from someone who knows his stuff - both your text and the video. In the video you linked to, it's great to see someone using visuals and speaking in an engaging and concise way. Rare on YouTube!! Would have been lovely to hear the instruments and the effects on them but that's a tiny niggle. Must go off and see what else he's uploaded.

I actually rarely use compression, isn't that awful? I just split up the sound into objects and process each one individually. But I sometimes use "parallel" compression, mentioned above. The attribution of this to "New York" engineers is extremely dubious, but it involves setting up another set of tracks. I also often add really dense, really short reverb.