An STD can be contracted and spread through kissing but that would only be the herpes STD.
Any other STD would only be contracted through sexual activity such as sex with a person who has an STD.
But it's a little possible to contract an STD through kissing if you kiss a person who has an STD and they have an open wound but that is very rare.
The most common way to get an STD is through sex but you can sometimes get an STD through other ways as well.