Start with statistics. Seriously, just google time series modeling (this seems ok for a beginner https://www.analyticsvidhya.com/blog/2015/12/complete-tutori...). Learn ARMA/ARIMA/etc.

Don't worry that just because it isn't using deep nets that it isn't state of the art or won't get the job done well. That would be like thinking python's built-in sort function isn't sufficient because it doesn't use Spark.