There are many ways to go about this, as mentioned above: BB/Crank, saddle, Wheels/tires/tubeless, air fork, stem, carbon seat post, carbon handlebar, etc.
Your bike is at the wrong price point to inexpensively lighten up. I recently spent $460 to shed 4 pounds from a steel frame AM hard tail just with a fork and wheel upgrade. At the end of it, it still weighed 28+ pounds, so how much is each gram worth to you?
Having said that, I have a titanium framed hard tail (still considered a heavy frame at about 3.5 lbs) that was built to around 19+ lbs with light wheels, tubeless 1.95 tires, carbon rigid fork, carbon seat post, titanium handlebar, and made into a single speed. Basically, the major components cost more than the frame. But that bike really sprints when I lay it on.
Bottom line... you can spend lots of money to lighten your heavy bike with "meh" results (like what I did with my On One EVO 456 II), or you can start off with a lighter bike altogether for lighter (not necessarily cheaper) results.
Picture time:
On One 456 EVO II
Untitled by
tk_1971, on Flickr
Untitled by
tk_1971, on Flickr
Raleigh MTI 1000 titanium
Untitled by
tk_1971, on Flickr