Ubuntu :: How To Install An Application

i'm new to ubuntu, and also new to linux.
so basically i have many many questions to ask.
so i describe myself as a new human being in this linux world.

today i found out when i download an application, it comes in "tar.gz" format,
so i searched for solution, and the only answer i get is to go to the package manager and download the package. well... that is not a relevant answer.

then i went to try out the firefox, so i found out that the firefox was out-of-date, it was only v3.5 , i went to help> and where is the check for update option, i was like huh!? where is that button? so i googled it and found out the update website, then i downloaded the file, before i open it, i saw "tar.gz" o.o!!??

nevermind, i plug in my pendrive to play some music, then the movie player came out and gave me an error message that i have to download some files to play this mp3 format. ok, i guess a 600mb operating installer doesn't comes with everything, and i clicked download.
dang! error! could not locate the file ..

ok, i switched back to windows, went to videos to search for solution on how to install tar.gz files. the video showed me, first you extract the file to anywhere, then you open the file, then you *blah blah blah* the terminal, type this command xyzabc^#*

so, my main question is how to install an application downloaded from a website?
don't tell me it's package manager because there are many things i can't download there.