It's going to take you awhile for the first week or two, then you'll get used to it and it will take you 5 seconds for each eye. Regular soft lenses, I assume?
I would recommend using your same-side hand to hold your eye open (index top lid, middle finger bottom lid), while using your opposite hand to put the contact in with the contact on your index finger. When you're more experienced you can just use one hand, index with the contact and middle finger to pull the bottom lid down.
Taking them out is easy even from the beginning. Pinch and pull, never understood what's so hard about that.