My wife is new to cycling too, She also had a bit of trouble to begin with.
Intially this was down to the saddle being too low. Which was mainly due to feeling safer with both feet on the ground, as someone has previously said.
with the saddle raised a bit you can still feel solid if you just, when stationary , lean the bike slightly towaeds your favoured leg and plant that foot down firmly , the opposite pedal should then be at the top with your foot on it for balance .
when getting on , move the pedal on the oppostite side to where you are standing to the top. Lean the bike towards you, hold a brake on , get your leg over and place the ball of your foot on the pedal, whilst keeping the bike leaning toward your standing leg . When that feels stable release the brake, and then , at the same time push the pedal with your foot on to the bottom, stand the bike up on move back onto the seat , and put your other foot onto the pedal at the top whilst freewheeling. With both feet planted you should then be able to start pedalling.
Dont start in too low a gear ( Low is big cog at the back small at the front) as the will mean that the first push from your non standing leg will whiz round to the bottom without the bike getting enough momentum for you to readily get onto the saddle and the other foot positioned . When moving make sure the gear you are in is not too easy that your feet are trying to play catchup, It shouldnt be so tough that you are labouring to get the pedals round but there should be enough resistance that you feel you are moving the pedals not vice versa.
I hope this hasnt come over patronising in any way, but I would rather tell you something you are already aware of than miss a tip which may help.
Good luck and keep persevering
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