How do invasions work?

I can't seem to find this spelled out anywhere...obviously soldiering and resolve play into it, but we can only load one guy on our transports in GC4 (as opposed to GC3, where you could load a lot more pop).  Does having multiple transports affect the invasion time?  Are invasions always successful given enough time?  How much does soldiering help?  

Any clarification would be appreciated!