"I have a lot of experience."
Translation:У меня много опыта.
With «много», you use the genitive case: мно́го опыта 'a-lot of-experience'. In fact, genitive case is often translated with 'of', so this is similar to the English usage.
"Есть" can be used when you ask if something exists (or state that something exists). - У тебя есть машина? = Do you have a car? - Да(, у меня есть машина) = Yes(, I have a car.)
If the existence of something is obvious or well-known, and it's a specific trait of this object that is discussed, "есть" usually is omitted. У него зеленые глаза = He has green eyes/His eyes are green ("У него есть зеленые глаза" would sound extremely awkward). "У тебя есть ... глаза?" also does not sound quite right. It's as if someone has a spare set of eyes and is questioned about it.