How to play with no lag on PC?

I recently bought a new gaming pc over amazon for $1000 and it really sucks in the "gaming" department. Whenever I play games that I've bought over steam, they lag like ****. Whenever I play any game it lags immensely, probably around 15-20 fps. In certain features of the game the fps is literally like 5 fps, such as zooming through a scope of a gun. The only game I can play that has no lag is Minecraft.

What should I do in terms of speeding it up to maybe, i don't know something like 80 fps?
Should I buy any better hardware? Is my RAM bad or my graphics card?

PC Specs:
AMD 6300 six core 3.50 ghz
RAM: 16 GB
graphics card: amd radeon HD 6670

With a computer like that there shouldn't be any lag. Before trying other solutions try the following:

1. Remove unnecessary startup items using MSCONFIG.
2. Download all the most recent drivers from the website of the manufacturer of your computer and from the video card maker.
3. Run windows update and download all those updates.

Hope that helps!

That graphics card is from 2012. This is why you don't buy prebuilts. I'd sell the card on craiglist or ebay and then buy a GTX 760 for around $260. It's the one of the best performance/dollar cards you can get right now. If you can't spend that much I'd get a radeon R7-265 because it beats the new GTX 750 ti.