Changing gears on bike-- problem?

OKay so i have had my bike for around a year now, not special or anything, not a BMX or Mountain bike just a normal kids bike from Halfords. Ever since the 1st time i rode it i've had trouble changing the gears. Every time i change it either the chain comes off, the chain gets stuck in between gears or it makes a noise. This bike was the last of its kind and was on the stand, so has no instructions, and had no warranty. We where told, when purchased, that we should come back in six weeks, but we live a while from there, so we never went back, so we have no warranty and it was never checked.(Our fault)
My dad, who isn't good with bikes, noticed that one of the three wires running from the handle bars to the back where the gear wires are is loose. If i had the time to get it checked out professionally- i would, but i am going out on a long ride tomorrow, and i need it to be ride-able and changeable. Sorry for my nontechnical terms, but if anyone could help me understand what COULD be wrong, i would greatly appreciate it.
 
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