Only getting 300 kb/s?

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I'm very new to owning my own computer, and am the only one in my family with any knowledge whatsoever. So I have to learn all that I can about how everything works. So please, bare with me because I don't know much.

I'm only getting 300 kb/s, which as of recently I find out is pretty pathetic. Many people I know average at least 4 mb/s.

My actual questions are these; what are all my possible options at increasing my connection speeds? How do I know what providers to look for? What should I look for when determining what is the best internet provider? How much do differing modems/routers affect connection speeds?

I know how to mess around with the settings on my router, I just don't know what all of it does.

My provider is At&t. Answering a single one of these questions would benefit me greatly, and I would be extremely thankful.
I forgot to mention, I have different speeds over the past year, but with the same provider. Some days I get 150 kb/s, but there was one time when I reached 1 mb/s, and averaged 700 kb/s for a time, what causes these fluctuations?