Some artists don't feel comfortable in their abilities or they get nervous at the idea of an unsatisfied client. But there are a few things you can do to make it go smoothly and to protect yourself while doing it.
If someone approaches you about doing a commission, you should feel flattered, they obviously like your art. But we sometimes question ourselves or we are afraid of getting ripped off in the end.
Nobody likes hidden prices, so the best thing you can do is to establish a price up front with the customer. You want to lay it all out for them. You can give them an approximate time line and how long you think it will take to do it (how many hours will you put into it). It's possible you have no idea how many hours. In that case you might want to establish a max price that the customer is willing to pay. If you're lucky, money will be no issue.
See the How to Price Artwork Section for more ideas on how to price your work.
An Artists nightmare would be to put time and effort into something and not get paid. To help avoid this you should always ask for a deposit. I usually ask for a 50% deposit, of what I assume the final price will be. You can always ask for a specific dollar amount, like $100 down. Or you can ask for 100% of the final price, if it doesn't take as long as you think you can refund their money.
A good system to use is paypal. They will help protect you and give both of you peace of mind.
Most people won't have an issue giving a deposit, they usually understand. But if they refuse to do it, you may want to reconsider doing business with them. You might even trust your customer and don't think you have to ask for a deposit, but I would still recommend it. I have done paintings for friends, assuming nothing will go wrong, then they delay paying me for months. It can ruin the friendship, as you don't want to be demanding, but you deserve to be paid. So it's still good practise to get a deposit from them too.
It's good to brainstorm with your customer, you want to ensure you are doing what they want. They maybe easy going and allow you to take control. But get a good idea of what direction to head in. How many characters/people, what type of background, what overall theme, what color scheme, etc.