SSL has been around for about a decade from its inception at Netscape. TLS is based on SSL 3.0, mainly so the IETF could have an open, community supported standard which could then be expanded with other Internet standards.
Basically, there isn't a world of difference between SSL and TLS. You will often see them supported in the same applications (SSL/TLS). They do not interoperate (one has to be picked at negotiation), but TLS can transform itself into SSL3 if necessary. As far I as I know, not much has been going on with TLS as a standard (it works well, just like SSL3). It was upgraded to comply with HTTP 1.1 and supports all the popular ciphers.
In server related projects, especially open source ones, TLS is basically superceding SSL. For clients, SSL3 is pretty much a standard (usually TLS is default, but it routinely downgrades to SSL3). You can support both TLS and SSL, so there is no conflict there.
You can make your own SSL certificate for encrypted communication with a program called openssl. Your server (of any type) will have documentation on supporting SSL/TLS.
A certificate only means so much, because it doesn't actually verify you are the indentity you claim you be. You could claim to be BusinessXYZ and actually be a scam artist. For third party verification, you have to use a service from a company like Verisign (not sure if they bought out all their competitors or not). Verisign is what is known as a Certificate Authority (CA), because they act as a third party to identify you as in fact you. Users coming to your site engaging in SSL/TLS communication will be notified by a prompt if your site cannot be identified by a CA. If you go with a CA, they can help you with all the details.
