Impress the professor in the classroom. Raise your hand during class and see if the professor calls on you. If you can show your adviser that you are capable in the classroom, he will be more trusting of you in the lab.
Show up on time to all meetings, and note if your adviser does the same. Certain people are habitually late, but your professor is more likely to be punctual if he enjoys working with you.
Ask your research adviser how you are doing. Allow him to give you honest feedback. Constructive criticism does not mean your professor hates you, but remember that the professors with whom you have a positive relationship with will be more than happy to outline your positive qualities than your negative.
During your conversations with the professor, notice if his attention is completely focused on the present moment. Research advisers typically are extremely busy, but if someone really likes you they tend to be more focused when you are around. Try to pick up facial cues and look for smiles.
Ask your research assistant if he can recommend you for any other research programs, internships or further courses of study at the end of your time working together. If he likes you, he will be more than happy to steer you in the right direction.