Question: “How do I handle a dependent variable with a lot of 0’s in regression?”
My answer: It depends. If the DV is a count, then you can try zero-inflated Poisson or zero-inflated negative binomials models
If the DV is continuous, then those methods are not appropriate. If it’s normal except for the zeros, you can try zero inflated normal models.
There are also hurdle models for various situations.