Tracy,
A sucker is natures way of trying to keep alive. If a plant is under stress it will sucker. Once you have cut a sucker out of the axils make sure you plant it in good soil mix and cover it with something to maintain a terrarium like atmosphere. I generally put my suckers into solo cups and enclose the cup in a covered ice cream dish which has a clear top. I check it weekly to make sure it hasn't dried out. If any suckers form on it I remove them as soon as I see them with a sharp tweezer or and X-Acto knife. Other than that it's about all u can do.
Fred in NJ

Tracy -

just to add a bit -

A. some plants are designed to sucker - they are trailers and should be grown multicrowned

B. Some plants have the tendency to sucker when they are young - and if with a help of Fred's technique you keep removing the suckers as early as possible until they mature - you are home free.

C. Some plants will sucker in your conditions no matter what - pass them to somebody else - very possibly they will behave better.

D. All plants sucker when stressed - exactly as Fred explained. Try to baby them a bit - and if it doesn't help - you can call them category C - and get rid of them.

TGIF

Irina

Tracy, check out the link below. Rachel has tons of cultural info and tutorials, with pix.

Good luck.

Korina

Here is a link that might be useful: Rachel's Suckers!