how can I utilise SQL Server tools to identify query optimisations, missing indexes etc?
No tool is perfect and you should not rely implementing the suggestions without proper testing your entire business life cycle.
Native tools like DTA are OK, but I have seen many problems with using it. I would not rely on it.
That being said, SQL Server exposes a wealth of information using DMVs and Extended Events.
I would suggest you start with : SQL Server Diagnostic Information Queries - Glenn Berry - choose as per your version of SQL Server.
Also, highly recommend this FREE book from RedGate - Performance Tuning with SQL Server Dynamic Management Views
You have to baseline your servers and then you can compare what is good and bad for your environment.
Remember performance tuning is an art, not science. It will take you some time to digest the resources I have cited and this is how I have learned.
You should be cautious when creating Missing indexes exposed by DMVs
Other blogs that contain a wealth of information are (in no particular order):