What is citation index? How are such indices calculated? How can any journal become part of an index? These are my questions about various indexes that are used at academic environments.
There is actually an entire field dedicated to answering the question about how to measure scholarly impact.
Two indices that you could probably compute by hand in a little bit of time are the h-index and the g-index.
Also, if you are an author thinking about submitting a draft, and looking for a good journal in your field, one place to look is on Google Scholar. Go to scholar.google.com, then click on `metrics'. Google has auto calculated the h-index and g-index for the last five years of a lot of different journals in different fields. Generally speaking journals with higher h or g numbers are going to be better places to publish. (Not an ironclad rule, so check with a trusted advisor before sending something out, but a good rule of thumb)
If you are an editor of a journal and you want your journal indexed, then just write to the editor of Journal Citation Reports and ask about the process to be included. Be prepared for a lengthy wait though.