Mentoring
So you're looking for a mentor, that's great! I've benefitted a lot from mentors in my career. It'll be a valuable experience for both you and your mentor. This post has my tips for finding a good mentor, asking them, and maintaining a good ongoing relationship.
Choosing
These are my three go-to rules for finding a mentor. They've held up across many companies and years.
1. Your mentor should be someone you admire. The best choice is usually someone the same career path as you, but further along by some years. They don't have to be so much more senior, it could just be the next step, but they've shown that they're willing and able to take on more responsibility and how to do it at your company. Ideally they're someone interesting, inspirational, and relateable.
Another type of mentoring relationship is when you're looking to make a change -- from Engineer to Eng Manager, or Eng Manager to Product Manager, say. Then you're looking for someone who made the switch. I find they're often the most eager to talk about how and why they did it.
2. Organizationally close-by is OK, but they shouldn't be one of your leaders. I've gotten the most out of mentors outside my chain of command. That way, I never had to worry about choosing my words (or topics) carefully. I could problem solve or just vent. Sometimes the person you need to discuss is your own boss.
3. Rapport is super important. Maybe the most important thing of all. Your meetings can't feel like a chore for either of you. Even if you've gotten along fine in the past, maybe you'll hit it off in this new relationship, maybe now.
How can you find the right person if it's not obvious who to ask? Use your network, talk to people, ask for referrals. Big companies often have mentoring programs for matchmaking.
Asking
While your mentor will benefit a bit, you'll be the one getting the most out of this deal. So it's up to you to ask. Understand that they're likely busy, so say how much you'd appreciate some of their time. Make sure they know it's OK to say no.
I recommend asking for a trial run to start with: "Let's do three or four meetings and then re-evaluate." That way you can make sure that it's clicking, see the "rapport" criteria above. If it's not feeling great on both sides then it's best to try again with someone else, no harm no foul.
Being A Good Mentee
So you've found someone, great. Here's some things you should do during probation and onward.
1. Respect their time. Be prompt. Work around their schedule and in a way that works best for them (30 min? over a meal?).
2. Come prepared with a topic or two, keep a backlog. It can be something specific, like problem solving a particular situation or relationship. Or it could be getting just-in-time feedback on a draft email or document. Or it could be open-ended, e.g. "if you could advise your former self 10 years ago, what would you have said?"
3. Check in from time to time. Make sure this is still working out for them: the style of meeting, duration, etc.
4. Find an appropriate way to thank them. Nothing big but it's important to show that you appreciate their time. For example at my current employer (Google) we have a system to give shout-outs to peers that come up at performance review time.
Finally, find a way to pay it forward. Introduce mentors and mentees; volunteer in your company's matchmaking service; find people who appear to stranded and offer to help them out. Sending this post might be a fine icebreaker.