In order to write an effective scientific paper, it really helps if you've had some practice reading and reviewing scientific papers. Some places you have probably received practice include: courses (senior undergraduate seminar courses and/or graduate seminar courses) and journal clubs.
Sometimes your mentor will also ask you to help review a manuscript. I highly recommend taking them up on this. The way I do this with my mentees is first send them the abstract and ask if them if they are interested in reviewing it with me. Then we each read the paper on our own, and each create a list of points that we want to discuss in a one-on-one meeting. During that meeting we will each go over our points, and create an outline of what the written review will look like. This outline needs to include: Summary, Major concerns, and Minor concerns. After that, the mentee will take that outline and make sure to add any extra points (usually the detailed minor concerns) and add a bit to the summary. Then they send it to me, and I go over it, editing and adding more to the three sections. Then I'll send the finished draft back to the mentee to read over and approve before submitting. I always list that the mentee aided in the review in the confidential comments to the editor when submitting. If your mentor hasn't yet asked you to review a paper, feel free to let them know you're interested. My best guess is they will be absolutely delighted to hear this.
This is an excellent resource for learning how to read and understand scientific papers. https://violentmetaphors.com/2013/08/25/how-to-read-and-understand-a-scientific-paper-2/