You are right. Often the best way to learn to speak a language is by conversing with local people.
Once you get used to the Glaswegian accent, I think you will find that the people are your best resource when it comes to improving your English skills. Scottish people are generally known to be friendly and hospitable towards foreigners, so you are sure to make some new friends as well.
If you want to go along a more formal route, you could investigate some options to doing some English lessons in Glasgow. The University of Glasgow offers free classes and the Glasgow School of English also has a number of courses tailored to those learning English as a foreign language.
Hope this helps. Good luck