Adding an outlet to a light switch, just want to make sure I have the right idea
All the bare safety ground wires in your box should connect together. It is not sufficient to take the ground from one romex and connect that to the switch and another one from another romex bundle to the outlet. It is best to tie them together at the back of the box with a good quality wire nut and have pigtails that come out to each unit.

The method to join into the existing white wires will be to use a short piece of white insulated wire that is stripped on each end (pig tail). One end will attach to the existing white wires with a wire nut and the other end to your outlet.   

For the black wire remove one end of it from the switch. Then attach two pigtail lengths of black wires to it with a wire nut and push that to the back of the box. One pigtail goes to the switch and the other to your outlet. 

To get the stray bits of wire for the pigtails you can either open up a length of surplus romex cable and pull out the individual wires from there OR you can visit a decent hardware store where they very often will sell individual wires by the foot.