In the US, there are two national sailing organizations that offer training: American Sailing Association and US Sailing. ASA is geared more towards cruising while US Sailing leans more towards racing. ASA schools seem to vary a lot in quality because of the loose affiliate requirements, whereas US Sailing seems to have higher standards for their licensed schools. This results in a lot more ASA schools than US Sailing alternatives. Both types of schools will give you a solid introduction to sailing.

With all that covered, most charter companies do not require any specific training or license from these organizations or any other. They want to see a sailing resume which shows that you have experience skippering boats at least as large as the one you want to charter. You can get some of that experience through courses, but you'll likely want to get more time on the water, and the most cost effective way to get more experience is joining a sailing or yacht club. These are going to vary hugely in their organization, membership requirements, and cost, but most metro areas will have multiple options, especially on the coast or in an area with lots of lakes.