on the left side of the screen there is a bar with options, one of them is Build Ships, try clicking that.
if you want to build in protection you will need to get hit first and afterwards the only thing you can build without leaving damage protection is starbases and scouts.
Note that ships have an upkeep so beside the initial mineral and cash cost you pay for them you will lose money for every turn you use after building, which very likely will take you into dept considering the nature of your question.