how can i increase the f/stop on my telephoto lens without just buying another one?

That is why faster lenses are made. I strongly suggest dumping that lens off on Ebay or something. Lenses that have a tremendous amount of zoom like that 55- 250 are always slow lenses. They are called slow because they require you to leave to shutter open for a long time. If you're shooting with a tripod and your subject isn't moving, its not such a big deal, but that isn't reality. That is why people prefer to buy fast lenses, fast lenses start at f/2.8. You probably bought the lens considering the price and how much it zooms. It's normal to think that way, but there is no free lunch. I don't own a single slow lens, and there is plenty of good reasons. I remember several years back a had a slow lens, I think it was a a 20- 85 or something like that. it was a f/2.8- 4 and I was shooting a Christmas party inside. Flash was not really an option as kids were sitting on santa's lap, and santa would have been blinded by hundred's of flashes. I dialed the camera in as best as I could, but no matter what I did, I was under exposing everything by a stop or so. I was pulling my hair out, wishing I had a faster lens. Within a week I dumped that lens and bought a 50mm f/1.8. The next year when the party came around again I was able to do the job better, but I was still at the very limits of the gear. f/1.8 was still not fast enough. I ended up buying yet another lens, the 85mm f/1.4. I still shoot the party, but that extra bit of opening up has saved the day, now I have the ability to shoot the party with plenty of room to nail the exposure. The 85mm f/1.4 is now my favorite lens. Its scary how good it is. Looking back at that slow lens, I realize how poor of a choice it really was.

One possibility is to buy another camera body that performs better in low light... but usually double the price only improves low light performance marginally. It is worthy to note that most new professional zooms are standardizing on f/4 constant aperture rather than f/2.8... because the old faster lenses are relics of film photography when we were limited to 400 ISO for most shooting.

But there is no way to modify the lens itself... it is as fast as it ever will be. Increase the lighting,

Nothing ... there is nothing you can do to increase the maximum aperture of a lens. Nothing at all. the only thing you can do when shooting in low light, once you've hit your lenses max aperture for that focal length, is to increase the ISO and/or slow the shutter.

Beyond that you need to buy good glass like Canon or Nikons 70-200 f2.8 at 2600$.

EDIT:

I'd like to clarify a few things from CDKey...'s response. The lens you have isn't un-usable ... it;s just not usable in certain conditions.

I own a 70-300 piece of crap Sigma lens and while I don't particularly like (not after shooting with L series glass so much) it still is a USABLE lens depending on the circumstances. I've shot at outdoor concerts with my crap lens and gotten decent results:

http://sphotos-a.ak.fbcdn.net/hphotos-ak-ash4/3782...

http://sphotos-c.ak.fbcdn.net/hphotos-ak-ash3/5642...

And if you are shooting with lots of light like a baseball game in full daylight or over cast day ... f5.6 is plenty wide (when looking at exposure).

What you need to do is understand the limitations of that lens and when to, nor not to, use it.

There is nothing you or anyone can do to change an f4-5.6 lens to something else except by buying a fast f2.8 zoom lens. If you want an f2.8 fast zoom then your only choice is to buy it.

You can't.

The widest it will go is f4 (at 55mm) and f5.6 (at 250mm).

As Scotty used to say on Star Trek - "You cannae change the laws of physics".

All you can do to get a higher shutter speed is to increase the ISO - an deal with noise in post.

You cannot, your option for low light is a prime lens

You can't make the aperture bigger than f/4. You'll have to raise the ISO.