Soooooooo basic.
Not even electronics, but basic wiring.
What is the best way to attach 2 wires together, assuming I don’t own a soldering iron? My whole life I’ve tried twisting them together, making little hooks out of them, and every other way I can think of. Electrical tape seems to help a little, but only a little. No matter what I do, they keep coming apart if I so much as look at them funny.
Added to this difficulty is the fact that the wires currently in question are very tiny.
You’ve answered yourself…
Specially for thin wires, buy a soldiering iron.
I’d go with a crimp on connector, like these from radio shack. That model is for telephone wires, which are pretty small. Shrink tubing is also good to protect the connection, easier than tape to use.
I have always just bound them real tight with electric tape. It works for me.
Crimp, solder, or use twist connectors, depending on your application.
I’m assuming that if the wires are tiny, you’re not talking house current.
If you’re talking house current (or any high voltage application), then you have safety issues that we haven’t addressed here.
I have to agree with the “buy a soldering iron” option. They are cheap and pretty easy to use for this application. I would twist the wires together, touch the twisted part with the tip of the soldering iron, and apply the solder to the touching point.
Upon preview I see other suggestions, but IMHO a crimping tool isn’t much easier to use than a soldering iron, and bad connections are less obvious.
Depending on the guage your best bet is probably a crimp on connector, you can get then at most auto supply places or Radio Shack. You can get straight splices or plug and socket connectors I find handy for things like the ground wire in a car stereo that might have to be disconnected. For things like 120VAC wiring a wire nut is probably the best way to go. In my experience just twist connecting small gauge stranded wire with a Western Union splice is often less than reliable. Soldering can be good if you do it correctly as a cold solder joint can be unreliable.
We’re talking about house current, but as run through a transformer. Seriously, you could touch the wires to my nipples and I still wouldn’t tell Jack where the universal remote was. 
The wires are for a Z-scale train set. The reason I dislike soldering for this is that it tends to use up wire quickly, and I need some good amount of flexibility in my setup. In other words, no permanent connections.
Z or G, soldering is the best way to go, with crimping second.
Are the rail joiners with the attached feeders available for Z scale? They work pretty well for HO…
No, you need special feeder track.
My favourite crimp connectors are “b” connectors, as seen here. (First hit I found, no clue about that retailer. We get them from the local industrial electronics shop.) They’re easy, reliable, and you can open them without cutting the wires.
What’s wrong with wire nuts?
I presume he’s working with 20 or 22 ga. wire. Ain’t a wire nut made for wire that small.
Well, I’m guessing it won’t have any more effect than the already-mentioned nipple procedure.
Sorry, the UL disagrees. Please refer to this chart for listed combinations of #22 and #20 wire with various Ideal wire nuts.
I’ve been an electronics hobbyist since I was seven years old. I’m now a 37 year old electrical engineer.
Crimps suck. Let me repeat: crimps suck. If I had a nickel for every time I personally witnessed a wire pulled out of a crimp I’d be able to buy a new FAL rifle.
Did I mention that crimps suck?
There are only two electrical connections that are any good. One of them is a good compression joint. Like a copper wire under lots of compressive force.
The other is solder.
A properly soldered electrical connection is a Good Thing[sup]TM[/sup].
Where the heck are you using crimp connections where there’s any way for the wires to be pulled? Without proper strain relief, yeah, they can pull apart, as can most anything else short of solder. But with proper strain relief, there’s nothing pulling, and hence no way for wires to pull out of a crimp connector, in which case they’re perfectly reliable.
I’m telling ya, crimps suck. Every time I work on an industrial wiring project there are two or three wires that pull out of crimps. Every time. And these were “properly” crimped connections using proper dies and proper hydraulic crimping tools. I’m telling ya, crimps suck. When a technician does an industrial wiring job for me, I explicitly tell them to solder every crimp joint. Other engineers are like you… “Crimps are great!” Um, nope. I don’t care what you think you know, or what others have told you. After crimping you should solder the joint.
So I’ll ask again. What sort of strain relief were you using? How are these joints going to be pulled apart if there’s no way to pull on the joint itself?