When I work with parents, I always tell them that children don't come with a manual! We don't automatically know how to parent them. We all learn from one another, from books, from parenting shows and videos, and of course, from our own children.
Two and three year olds are naturally self-absorbed...it's me, me, me. That's normal for them. They don't have any ability to delay gratification. That comes with maturity...a few more years.
So, it's up to the parent to help children with these skills before they can use them themselves. In fancy terms, it's called emotional regulation. The adult, in this case YOU have to be the one that decides for them when and what they can have. Yes to one cookie, no to ten! You put the structure in place for them now, and eventually they will be able to structure themselves.
That's what discipline is: creating rules (limits) and structure for your children. Limits make them feel safe and secure. Find a good balance between permissive and very firm. It also depends on the temperament of your child. Some need a more firm hand, while others will fall into line easily with gentle guidance.
With regard to your toddler crying when you begin to leave him, this also is very normal. Your son is attached to you as the caregiver. When you begin to ask him to share you (so you can go to work etc) he won't be happy! But the staff in the learning center are skilled at helping children say goodbye to their parents in the morning, and re-unite successfully in the evening. Ask them for help. They will also reassure you that when he is crying as you leave, he probably stops a few minutes after you're gone. Pay attention to "the reunion." How does he behave when you pick him up? Is he happy to see you? Is he angry? Does he avoid you? If he's happy, that means he likely has a strong attachment to you, and is doing fine. If he isn't, ask the staff for help.
Do check out some parenting books at the library to help you with discipline. I recommend Dr. Sear's books on child-raising, including his on Disciplining your child. Any book on attachment parenting will also be useful.
Your strategies of time outs are good (time ins, where you stay also work), and withdrawing privileges (or toys) is a good way to teach consequences. Don't let them cry...it just ends up hurting your bond, which is harder to fix down the road.
I hope this has been helpful.
Mary Lynn Trotter MSW RSW