Carefully. That's my first suggestion. Money's a touchy subject, and marriage counselors will tell you it generally tops the list of things that couples argue about. So, if you're thinking about asking a friend or family member to invest, I advise you to be selective about who you approach and cautious about how you handle the matter.
For me, the first order of business is deciding who to ask. Even if I think I have a great opportunity to put in front of somebody - one that could ultimately make them a lot of money - I wouldn't approach them if I didn't think they were in a position to lose it. No matter what anybody tells you, every entrepreneurial venture involves risk - some more than others, but all to some degree. So when calculating risk, I always imagine the worst-case scenario and decide whether I can live with the outcome if it doesn't play out.
I know I definitely couldn't live with it if an investment I recommended to someone close to me tanked and they lost their life savings. Not only don't I want the burden of worrying about whether that might happen, I don't want to shoulder the guilt if it does.
Which brings me to another key issue to consider: you need to think carefully about whether you're prepared for the relationship to change as a result of your request for money, because more than likely, it's going to change.
I'd also look at whether they're the sort of person to take financial risks. I've had people say to me many times they'd love to invest in some of my projects, but if I know that person to be risk-averse - let's say they've only ever bought GIC's and T-Bills - I know they'll probably be too anxious about their investment to enjoy what may turn out to be a roller-coaster ride. Not to mention I don't want the responsibility of holding their hand the whole way!
Because money issues are so fraught with emotion, I find if you're the least bit nervous about entering into a financial relationship with somebody, you shouldn't do it. With family, the issue can be particularly sticky. It can cause tension with parents and siblings can get upset if they think you're taking what they perceive to be their future inheritance. It's fine if it winds up increasing that inheritance, but it's not so fine if it depletes it.
Of course, you're not the only person who has to wade through all the psychological waters that surround the decision to enter into a personal financial relationship. The onus for the investment lies just as much on the person making the investment as the one asking for the money. Somebody close to you may feel real ambivalence about investing, but feel obliged to do so. I tend to think of funds invested out of guilt or obligation as "muddy money". Muddy money can really weigh you down and - in life and in business - I try not to step in quicksand.
In the end, whatever you choose to do, you can't afford to ignore the psychological issues. Just remember that money always comes with a price. You need to decide whether you'd rather pay it in dollars or emotions.