Regular Expression is a pattern that allows you to validate the user's input text, such as email, password, etc. To use regular expressions, you should define the pattern that you want to identify in a text stream by using the syntax documented in Regular Expression Language - Quick Reference

string email = @"^\w+@[a-zA-Z_]+?\.[a-zA-Z]{2,3}$";
string input = "";
bool valid = Regex.IsMatch(input, email);

Similarly you can validate your phone and zipcode with the patterns below

string phone = @"^[2-9]\d{2}-\d{3}-\d{4}$";
string zipcode = @"^\d{3}\s?\d{3}$";