Write a short (one page) summary of the paper, giving key results. Include any important insights you obtained by reading the paper. End your summary with questions you might have that the professor might be able to answer. Send a copy to the professor.
Note that in some fields like mathematics, the "key results" might include things not stated as such. An interesting and unique proof technique or methodology might be the most important contribution.
The insights and questions are just as important as the summary, actually.
If you have periodic meetings with the professor, bring the summaries along with you.
Bonus: If you can think of some logical extension to the paper that might require research, mention that also.
Going beyond your question, it would be useful personally if you add the paper to a personal bibliographic list along with your summary. Perhaps include things referenced in that paper that you think would be worth exploring.