You enthusiasm is quite nice, but your explanations are a bit vague, I think, for someone who is just starting out.
After untarring a file, make sure to read both the README and the INSTALL files that are in the newly created directory, which should be similar to the tar files name.
More likely than not you then need to use the ./configure command.
Heema wrote it all out quite clearly.
What you mentioned about an installer does bring up an important issue. You may be downloading a compresed binary file. In that case you will install using an installer file. Mozilla comes to mind.
Again, for the most part you will do as Heema wrote.