I'm a bike tech at dicks sporting goods in Bloomfield, MI and I'm having trouble with replacing the cables on an old 10 speed freestyle. I've only been working at this job for about 3 months now, so I don't have a ton of experience working on bikes yet, and I can't tell how to get the cable out of the shifter.
It looks like the cable should just be able to pop out of the end of the shifter (I have already removed the housing), but I can't get it to budge. Is there something else I need to do first before I can take the cable out, or is it just that this particular one is likely jammed?
On most shifters, you just push the cable out of the shifter (in the opposite direction that the shifter pulls the cable normally) until the cable head pops out and the cable can slide out completely. It may just be the the head on the cable is wedged tightly into the hole in the shifter and needs a little force to pop out. The sizing of the cable heads and shifter holes isn't completely standard and you sometimes get very tight ones.
There are a multitude of levers on the market, and we don't even know if the bike has road or mountain bars. Need info as to brand/model and pics of lever.
Excuse me, but we only know what you tell us, and if we don't know anything about what lever you are dealing with it's difficult to give specific advice. You still have not said what type of shifter you have or provided a pic.
From what I have seen this year in bicycles and from this spread, is that Dicks bikes are just a cut above Walmart/Target /Kmart type bikes. 100% due to no training, and the training that is provided is rather low quality. @ least the op is trying to find out how to do it. Keep going guys, rather enjoyable so far!
There are two kinds of people in the world, "Those who help themselves to people, and those who help people!"
Again, I don't know what kind of shifter it is or I would have just looked up the manufacturer instructions for how to change the cable instead of creating an account for this website cny... I'm at work and do not have a way to take pictures. The lever is very basic in design though; I was already fairly sure that the problem was that the head of the derailleur cable was wedged in too tight, and just wanted to confirm what I thought, which Dave did.
You are right Painkiller, the training here was very subpar :/
If you could get a pic, I could tell you what to do. but if the cable is a normal shift cable like used on mtb and road sti type shifters. dis connect the cable move up to the front housing cut the cable about an inch longer than the housing, making sure the housing is in the shifter, lock cable in a drill (leave small gap), grab housing firm and just pop the drill trigger quickly rev and forward til it pops loose. be careful, it will windup
There are two kinds of people in the world, "Those who help themselves to people, and those who help people!"
All they say on them is Index Shifting System, which could be about any brand. 
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