Realistic journal choice is a good place to start. Get a sense from the doctors you're working with what journal they think might be good for the case report. Read several recent case reports from that journal and consider which elements are things that you'd also like to include. Read the author guidelines closely to make sure that what you write/ your figures adhere to them. Get feedback from the senior author and anyone else whose opinion you'd feel comfortable asking for early on, and then send out a polished draft to all authors with a reasonable deadline to give you comments/edits (3-4 weeks). Check if the senior wants to be corresponding author or wants you to be, if they have any suggestions for reviewers (as many journals will want you to provide 3 potential reviews), and ask if they can help you draft the cover letter (or at least give feedback on one you've drafted). If you are doing the submission, prepare yourself for a ridiculously user-unfriendly process. Send the submission PDF around the all authors and give a few days for them to point out any final edits. Submit and prepare to wait. Sometimes rejections are fast and sometimes they take weeks, which is frustrating. If rejected, don't take it personally, incorporate any useful feedback from the editor, reformat for another journal, send around again (can give less time if most changes were only formatting) and resubmit. If the case report is not rejected, congratulations, and be prepared to address the asked-for changes or defend why you think they aren't necessary (super diplomatically).
Timeline is not always predictable. However, if journal choice is reasonable and the revisions are minor you are probably looking at 4-6 months from time of submission to online publication. Good luck!