Hi I am havein a little trouble with the expeditions. how do you do one? and what is it for?

An expedition is a gamble. You send some ships to explore outer space and they will bring back res or more ships, get destroyed or partially destroyed, or nothing will happen. To do one, you must first get expidition tech. After you do, go into the fleet tab and choose some ships, then hit continue. Send it to planet slot 16 and hit expidition. I'm not sure what hold time does.

Just for the record I would not recommend doing them.

so would leveling up your expedition tech would improve your chances of a good return ?

No, it just increases the number of fleets you can have on expedition.