Assuming that the pedal and cleat are in good condition,(i.e. not broken) the only thing that will help is practice. Lean up against a wall and clip in and out with both feet. Get it down so that you can clip out without thinking that you're clipping out, rather, that you're putting your foot down. Then move on to the ubiquitous grassy field and practice some more at various speeds, and "sudden"stops.If you get this far, riding out in the world is easier. You usually know when you need to stop, prepare for it, clip out one (or both)when you see a need to stop.I usually unclip one side if I'm in slow traffic or on a MUP with unpredictable traffic(read dogs&kids) Don't go back into traffic unless you're confident in your ability to get in and out. No sense in getting killed over these things.
Apart from that,many pedals have some tension adjustment for the pressure needed to clip out, make sure yours are set to light for now. Read the manual that came with them. Eh, that and the occasional drop of lube on the cleat to keep things smooth.