I think the pumps that advertise that they do both types of valves have an end part for the prestas that screws on and off. You take it off for the schrader valves. At least that's what my floor pump does. If you jam your Presta pump adapter onto schrader valves you will surely wreck the rubber gasket there and need to buy a new Presta adapter end.
Also, make sure the parts on the end of the pump hose are screwed on all the way. Mine were loose for a while and the pump didnt work well until i discovered the problem and now it works well again.
Are you "priming" your little presta valve before you stick the pump on it? You first unscrew the golden valve tip to the "open" position (doesn't come all the way off mind you), then push it down lightly just for a second to let a little poof of air out- this primes the presta valve tip itself so it will work properly when you start pumping for real. The poof can be startling the first time you do it.
When you are done pumping, get both thumbs under your pump end and try to pop it off the valve using thumb leverage QUICKLY and evenly- don't wiggle it from side to side on the valve or you'll break the valve tip and have to get new tubes.