In short, no, there is no better way to play with strings other than regular expressions unless you are using a library/package that provides out of the box functions to use. Their utility/importance is simply reflected by the fact that they are available in all languages in one capacity or the other.
Here is the long answer.
Your question implies that your problem is not limited to validating an email address but rather validating strings using regular expressions.
First off, for an alternative, you can surely break a string up and treat it any way you like. All modern languages have a comprehensive list of string functions that you can use. However, you should also know that it will not be worth the effort and will make your code look messy.
Ultimately, you will wonder is there an easier and better way to do this to which the answer will be regular expressions.
As for them being hard to learn, I have met software professionals who have 10+ years industry experience but still use Google for their regular expression needs so you are not alone in that regard.
The only way to get better at them is to keep learning and practicing but isn't that the case with every skill?