Like anything to do with a startup, it's about proactive outreach. AngelList is a great way to research what people have done before. You want to optimize for relevant experience. AngelList however is very ineffective for making cold connections. Instead, I use LinkedIn and ensure to always write a personalized introduction with my connection request explaining why my company is something they would be interested in.
After the connection is accepted, I then follow-up with a personalized email thanking them for accepting the request and then asking to buy them a coffee or schedule a meeting.
I have built a great network of both formal and informal advisors and investors through this process.
Formal advisors really should be limited to just a few. In these cases, granting options to purchase equity between 0.5 - 1% is standard for great advisors. But reimbursing expenses is far less standard. I'll always offer to pick-up the tab as a sign of respect for their time, but other than that, advisors (myself included) are generally happy to pay out-of-pocket unless for travel.
Just like any relationship, be sure that you want to make a long-term commitment in equity before formalizing the relationship. Often, good advisors where there is a mutual chemistry will be happy to do many meetings without anything committed.
Lastly, I would caution you to be wary of people who approach you to act as an advisor and/or people who are actively operational and also on many advisory boards. I limit myself to a handful of formal advisory relationships at a time and it's usually owing to a longstanding friendship that I am an advisor. You want your advisors that you're paying equity to to really be engaged.
Happy to talk any of this with you in a call.
I have been mentoring and advising early companies and startups for a while now... It is mostly done through some organizations - alumni or University mentoring services, state or local, or some specialized mentoring groups and services. Most mentors are volunteers and usually they are not allowed to be "compensated" by companies they mentor. Advisors on the other hand are usually compensated for their time (more often with equity and expense reimbursements).
If you do not know an appropriate organization that could help you find mentors and advisers - reach out to relevant experts in your field or academics. People usually are willing to talk and if you like what they are saying you can discuss formal arrangements.
Ask is important. Always reach out to people who you believe could be great mentors to you and be specific in your ask for example, don't just ask "please be my Mentor" be more specific then that as to what help you are looking for, expectations, time commitments etc.
There are specific organizations who you can reach out for a Mentor match as well, for example, if you're a young entrepreneur in Canada, you could reach out to CYBF Canadian Youth Business Foundation www.cybf.ca or in US you could go for SCORE http://www.score.org/mentors and many more.