Soldering the end of the cable is only necessary if you're trying to reuse old cables. The solder is just to prevent the end from fraying while trying to poke the cable into the hole.

Just make sure that you're attempting to thread the cable into the right hole, make sure that its shifted to the positions at which the cable would have the least tension possible, and then just keep poking and poking and poking. Sometimes all it takes is just a bit of time and perseverance; theres no real skill or finesse to threading the cable into a shifter. Though, it may help if you can take a flashlight and look for the hole, then at least that will give you a visual cue as to where the hole is.

The important part is just making sure you haven't shifted at all on the new shifters. If you're installing the right shifter, click the shifter all the way down as if you were bringing the chain to the smallest cog. If you're doing the left shifter, shift it all the way down as if you were shifting to the smaller ring.