You can improve your grammar by reading a lot. Any kind of reading of reading materials which sought your interest. Reading books along with studying is the best way to grammar and communication skills.
Yes, reading and speaking are the best ways to improve your grammar usage. When you’re listening to other speakers, or reading articles (interviews are particularly good) you can begin to notice different grammatical structures that are used and then start trying to use them yourself. It’s probably best to focus on one structure at a time, one that you know you have problems with - the present perfect for example, or conditional sentences.
Note how the tense is formed when and why it is used and this will help you to understand its function. Investing in a good grammar reference book is also a good idea so that you consolidate what you have noticed when listening or reading. I would recommend the English Grammar In Use series by Raymond Murphy as a good resource.