Hey Petrokov!

Well I gotta say, you've kinda got the hardest part out of the way: you in fact knew it wasn't real. My suggestion is to start practicing reality checks during the day. That way, the next time you feel "this isn't real" or "something just isn't right," you can perform one. Upon a successful check, you will turn your realization into a DILD (dream induced lucid dream). Some popular checks you can do are listed here: Reality Checks.

Good luck on getting that full lucid, and don't hesitate to PM me if you have any questions.