1995 Chevy Cavalier shiftiing

Does it have a button on shifter you depress to get into park?

yes it has between seat shifter. You depress button to move into all gears.. Car shifts fine when driviing. It also shifts well into all other gears. It will go into park but then it doesnt engage. we have been slowly letting it roll ,either in drive or reverse ,and then shifting it into park. It will then engage. what could it be and is it expensive to fix?

First check the shifter cable, have someone move lever through range and watch shifter lever on trans.
It could be the cable is binding or a bracket is loose.

Worst case would be the parking "pawl" is worn, it is a small "hook" inside trans that locks trans in park. It could be worn or cracked.
These, however, rarely go bad unless you were to shift in park when moving.

Also the button, which you use to shift into park has a plastic piece that can wear or break. You would have to remove the shift console to repair.