It's a beautiful practice, whoever you are and it's a crucial part of the Christian life — every Christian.
Imagine everyone's thought life was a pie chart. Most-likely we'd all be shocked at the crummy things we get stuck dwelling on, but we all do it... worries about the upcoming day, that thing that person did a while ago, an area where we wish we'd done better. In a sense, those things can become mediations, just not very helpful meditations.
A savvy Christian will recognize those unhelpful mediations and replace them with good ones. It's quite similar to diet. You ought to replace the midnight twinkie habit with, say, a glass of water and an apple (and then hopefully nothing at all). Then, you ought to add good eating habits, like oats in the morning and plenty of greens during the day. With diet the health of your body is at stake. But in the case of thoughts, it's the health of your soul.
So, start noticing that pie chart and see what may need replacing. Perhaps you could even set aside a specific time of day just to think something good for a while. For example, perhaps you find self-loathing, shameful thoughts creep into your mind many times per day. You could begin your morning by pondering how God called humans "good", that God paid Jesus' blood for you and that you are, spiritually speaking, royalty.
This is just one idea, of course, but we all have areas that need work. This is part of "taking every thought captive." It's a massive task, but fortunately we have His help.
(For bonus points, ask God "What thoughts in my life needs replacing?" He may just tell you.)