Define "out of the US" - you mean Caribbean, or further away like the Pacific and SE Asia regions? Do you already know where you want to go, or have no idea? There is no one answer or site and it really depends where you're going and how much help you want or need. Organized dive shop trips as mentioned can also be a good option.
For the Caribbean, I think your best bet is to do lots of research and pick the place you want to go. As you read stuff on Scubaboard or other resources, you will start to get a picture in your head of what is available and what you would like, and gradually add to that picture. After a bit it will seem less overwhelming and you will develop a list of places you'd like to go. Then just book what you have decided however their web site tells you to - booking most places in the Caribbean is very straightforward. Look for your plane tickets starting with some site like Kayak or Expedia. Some islands are a little harder to get to than others and you may need or want to use some regional airline that doesn't show up in the big search engines. (Or now Southwest Airlines, for some places.) You can usually find a "how to get here" page for a destination you are interested in that will give you the latest scoop quickly, either on some tourist bureau website, or on the sites of some resorts.
You can certainly have one of the dive travel agents do all this for you if you prefer that or just don't want to be bothered, but I find that's not less work and may result in a less satisfactory experience. You need to do the research anyway and not just go where some agent suggests. Their websites can be also be good resources, but they often focus on booking certain places. And if you've done the research and know where you want to go, I think it's easier to just book instead of involving a middleman. (Occasionally some of the agencies will have discounts available that you can't get on your own and may make it worth the trouble using an agent instead - Maduro is one that comes to mind where I think I've seen this. but I'm sure there are others.) I find booking plane tickets is easier when I am looking right at what is available and can choose what works best for me instead of playing twenty questions with someone. On top of that there may be a fee for an agent to book your air. (Another exception - there are some instances where it's hard to book some local flight or other transportation. Sometimes a resort may help, or finding and contacting the right agent can makes things easier. You will figure this out as you go along, like when you can't figure out how to get to someplace. Utila is one place comes to mind.)
More "exotic" destinations can be another matter, especially if you haven't done it before. Some will be as easy to deal with as going to a mainstream place in the Caribbean - pick the place, book directly, buy plane tickets, done. Some places are really helpful dealing with quirky local logistics and make it easy, others will leave it more up to you. You may run into issues dealing with time zones, language, and payment, or simply lack of useful info on websites. You may need to use some local airline that you can't really book online yourself, or you could except their website is only in a language you don't speak, or whatever. When you get to this point finding an agent that deals in that region might be the way to go.
I can't really list agents since I don't use them much but I'm sure others will have suggestions. Reef and Rainforest is one I've used and I was happy.
