Depends on what "school" you follow - Me, I anchor the tool on rest (Typically left hand, but I am slowly training myself to be able to use either hand) and press down on the tool into the rest - absolutely no force pushing into the cut, right hand holding handle anchored to hip and then use body weight to move the gouge along the rest - so pressing down only enough to just keep gouge firmly against the rest as it slides along. (That is, I don't direct the cut with anything but body movement for the most part, so stance and learning the turner's dance is important with that)
As Dean mentions, it is entirely do-able to do those cuts both inside and outside a bowl with one hand only on the tool handle (should not be pushing the tool into the cut - you just touch the tool to the wood and guide it while it cuts at its own speed) - so as I mention, I only use enough pressure on the tool (downward into the tool rest) to keep it steady and keep it from bouncing around... If you find that you are having to push the tool INTO the cut in order to make any progress, then you've got a dull tool, or you haven't mastered floating your bevel while pointing the flute (and bevel) in the direction you want to go.
Dean's final word on it really is the best answer if at all possible, find a mentor or club or someone experienced that can stand at the lathe with you and provide guidance. (Unfortunately, I do not have that luxury myself, so I am taking 5x as long to self-learn techniques that mentored beginners pick up rather quickly)