The major online poker sites all have a variety of ways in which you can deposit money with them. Makes sense, of course - they don't want to make it difficult for you to become a customer. Perhaps the easiest way of depositing, when it's your first time, is by using a credit card. Visa and Mastercard are pretty much universally accepted, and you'd be hard pressed to find a site where they aren't viable options. However, even though the sites themselves rarely have a problem accepting your credit cards, the credit cards themselves may. It's not uncommon that credit card companies do not allow transfers to or from gambling sites. This, as far as I understand, is mostly just a problem in the U.S. (see our poker sites accepting US players page)
If your goal with online poker is just to play and have fun, for a minimum amount of money, then depositing through the use of a credit card (if you're able to) is probably the most convenient way of going about it. If you plan on playing a lot, and possibly at many different sites (which would necessitate a fast and easy way of moving funds around) then you would do well to get yourself a NETeller account. It's my preferred way of handling online funds, and I believe most of my friends who play extensively online feel the same way. It will also resolve any issue you may have with poker sites and your credit card company; you can deposit money into the NETeller account using your credit card, and then transfer that money into the poker site. Depositing to NETeller using a credit card does carry with it a fee, though, so make sure to read the terms and conditions first.
Depositing at PokerStars with funds from NETeller
But about depositing to poker sites - is it safe? Can you trust the poker sites with your money? I'm hesitant to make guarantees for any of these sites (because I don't want you to be mad at me if you run into trouble), but as a general rule of thumb the answer is a doubtless "yes." If you deposit at a site with thousands of players, you can be reasonably certain that there's nothing fishy going on; all those players wouldn't be there if there was. I've never had any problems with money online, and it's not often I hear about it either. Keep in mind that it's in the sites' best interest to make sure everyone knows they're trustworthy; their business depends on it. If you're curious about a new site, or one that you haven't heard from before, drop a note in the forums and ask if there are any regulars who play there, and how they feel about it. Do a quick forum search first though, and see if there has been discussions about the poker room you're interested in already - chances are there has been.
If there's anything that you're wondering about when it comes to terms and conditions, or methods of depositing/withdrawing, never hesitate to contact your site's customer service, either via email or phone. They are usually very quick to respond, and will in most cases be very helpful. Remember, you're the customer.