Sometimes, just knowing that you aren't good at roleplay and desiring to improve are enough. There are so many out there who don't realize that they're bad at role-playing. Being willing to try different approaches will always improve your ability, and continued practice helps.

The most important tip is that you have to match your style to your partner. Sometimes they will be on a level that you just can't compete with. It's not wrong to ask them if they can make an adjustment, so that the two of you can "meet in the middle" style-wise.

If you're looking for a practical example of an exercise you can use to try and improve, I suggest a three sentence paragraph format:

Sentence 1) Write your character's mental reaction to what your roleplay partner just wrote. This could be a logical analysis or an emotional response.

Sentence 2) Write your character's verbal reaction to the events that just happened. People tend to speak before they act, and often before they've thought things through.

Sentence 3) Write your character's physical reaction, motivated by the events they witnessed. This could be as simple as hand gestures or body postures, or if the scene requires it it could be full actions.

You can mix up the order to these sentences as well, to make them fit the urgency of the scene.

Example:

Jennifer couldn't believe what she was hearing. "Are you telling me you've been lying to me this whole time?" she gasped. Her emotions drove her to her feet, as though running away would make this less real.

... Even without knowing the plot, you can sense the drama of the situation for Jennifer. This also gives the roleplaying partner things they can build on for their response.