1) Align all incentives. Make sure that the mentor/adviser is not working with a competing start-up, does not have board membership on another company that could cause a misalignment. If the adviser is from the venture community, I would ask around to see what companies they have been actively engaging, what companies they recently funded.
2) Require regular meetings. A lot of entrepreneurs that I talk with have great advisers and mentors to lean on, but talk with them so infrequently that they are not successful at leveraging their expertise and connections. To maximize the time and relationships that you have, I would schedule bi-weekly calls and monthly in-person meetings with all of you mentors and advisers. And, if a mentor/adviser is not willing to meet that often, then it should be seen as an indicator of how helpful they will be in driving your business forward.
3) Don't offer equity or payment until the adviser says something. The start-up ecosystem is such that people are willing to do a lot of work and mentoring without compensation. Before you are willing to give up that valuable equity award, make sure that you work towards a non-payment agreement first.
4) Identify your needs from this person before you develop the relationship. Most mentor/adviser relationships fail because the entrepreneur hasn't identified what the needs are from the person with whom they are talking to (it is also pretty frustrating to be on the other side when this happens). Advisers and mentors can be valuable in more ways then just making introductions. Many times, these people have built teams, businesses, made sales pitches, etc. Use them for everything that you have not done before.
5) Have an end goal. For any informal relationship to work, I believe that their needs to be an end goal that everyone is working towards. It could be anything from raising the angel round to successfully selling your product to a strategic customer. Regardless of what the end goal is for you, make sure that you have decided on final outcome that you want to see from the mentor/adviser relationship. And, once this final outcome is achieved, celebrate and move on. There is often a feeling that these relationships should last for ever. In my opinion, that is not necessary.