The "handle type thing" is a Tremolo or, more often referred to as a "whammy" bar. The thing at the base of the strings is called a bridge. Looking at the strings, there should be a hole to the right of the smallest string. If your "handle" is threaded, stick the threaded end into the hole and rotate in a clockwise motion. Once is hits the bottom of the threads, back it off one turn and gravity will let it hang out of the way while you play. If there are no threads, it will slip in and you will feel a "click" when it's in the proper position.
On the back of the guitar, there is a cover plate that covers the cavity where the springs are located that make the "whammy bar" work. The springs hold tension on the bridge so you can tune it and play normally, but let the "whammy bar" stretch or release tension on the strings when you push or pull it. If you already have springs inside the cavity, the extra spring you have will let you add more tension to the bridge, but you probably won't need it. If there are no springs already installed, you can install your "extra" spring in there to give you the flex and spring for the "bar-handle" to work properly.
To install a spring, loosen or remove your guitar strings, open the cover on the back, and install the spring over the hooks on the bridge and the hook on a metal bar on the other end of the cavity. Replace the cover, insert your "handle", and wiggle-away.
The allen wrenches are most likely for adjustment of the moveable pieces that support the strings on the bridge. The bridge has adjustments for up and down, and forward and back to adjust the height and distance where the string is supported. Don't adjust the bridge supports unless you loosen the strings. It is highly recommended that you don't make any adjustments yourself unless you are familiar with the mechanism. You can adjust your guitar where it's impossible to keep in tune if the adjustments are not perfect. There are usually guitar repair shops close by and offer "set-up" services to get your instrument adjusted properly. It's well worth the money to have it done right, and the service people with often teach you many things that will help keep your instrument playing well.
Hope this helps.