One person's perspective:
1. Most professionals, at least in my experience, get that it can be intimidating for a student to come up to them. Being in those shoes before, many are approachable and excited to hear from enthusiastic students. Just follow basic social rules, and you're already starting on the right foot.
2. If your mentor or someone else you know is going to the conference or event, they can be of help if they know people. Let them know either ahead of time who you would like to meet or what types of people you are looking to meet. Having a third party introduction not only makes for an easier icebreaker, but you're also being vouched for in a way.
3. Don't go into meeting a person with the hope they are going to offer you a job that day. A lot of professionals at conferences or events like to socialize during breaks. Turning the conversation into a job solicitation right away can come off a bit intense. Plus, remember... They don't know you, yet! It's ok to keep early conversations basic: research or clinical interests, what they are currently up to, how they like their institution or region, etc.
4. If you meet someone at a conference for 5 minutes and don't talk to them for months, don't expect them to remember you. It can't hurt to email them not long after the conference, remind them which student you are, say it was a pleasure meeting them, and have a follow up question (or request presentation slides from the conference, if applicable). They still may not remember you the next time, but it increases the odds.
5. This is the big theme of the last two, but it's crucial: be patient. Networking is a gradual process, not an isolated incident of schmoozing. Start early, be genuine, and be proactive. Remember that these things snowball too; knowing one person makes it easier to meet more people.
6. Last addition, since you asked about things to talk about. If you do eventually ask about job opportunities, this is much easier if the conversation first comes back to your overall professional interests. If you are currently or soon on the job market, it is ok to say that. If wanting to ask about an opening, unless you are asking about one you specifically know of, keep this part general: inquire about any potential openings they know about that fit with your interests, as opposed to any openings at their institution. You can also ask them for their own advice... This opens the door to talk specifics about your interests.
