Can one improve his/her english skills?

It is definitely possible for one to improve his/her english skills. Nothing is impossible. To me, a language is a skill that has to be acquired over time. No amount of tuition will help you to improve if you yourself don't work hard.
Basically, some effective ways of improving your english learning skills is through knowing your capacity to learn, your interest, and knowledge of what you wish to learn. You must first be motivated and interested to learn and not give up easily.
Some ways of improving one's english skills is by doing your homework and handing them in on time, reading different genres of english books regularly, make it a point to read the newspaper everyday and take note of new words and their meanings, so you learn new words everyday as you go along. You can also watch the news through the television.
In conclusion, there are a thousand and one ways to improve one's english skills, but it is all up to the individual whether he/she is willing to learn and to apply the skills effectively.