In the next few weeks I'm going to be trying to connect new rear turn signals and a new brake light. I've never done wiring so Im asking for pointers, and what stuff I'll need to do it right. Like should I get solder and a soldering iron, or any stuff I'll need. I'll post pics of the lights I'll be using so you can guys can better help me out, thanks!

..or if you're really lame, like me... you'll find a bunch of wire nuts under the seat...
... right next to the burnt wires... ...

You want my advice?...
...of course you don't... ..

I solder nearly everything. If its in a harsh environment or something OR,  IF it fails, Im screwed, I solder it.
One of the quickest ways to solder something is with  butane soldering iron, Lowes has them for less that $12.00..

Heat shink tubing is a shop necessity, as is Liquid Electricl tape &, of course, the REal Electrical tape.. dont buy cheap tape, not for electrical work you want to last.

To make a splice, point the 2 stripped wire At each other, wind from the center, toward the other wire,, Dont lay the wires side by side, with the stripped wires both pointing up, & twist them, that way, the wires will be in a straight line & you an slip a section of Heat Shrink on One of the Wires,, BEFORE you twist those wires,, sorry,, I got outta step,,

Anyway, strip the wires, ( if youve got a smidgen over 1/2 of wire pokin out on each wire, youre golden) put heat shrink on one end, twist the wires, apply soldering flux( Paste, available in many places) to the wire ends, heat the wires, try to not melt the insulation, maybe for a newbie, a soldering iron would be a better choice, A Biggo Fat Weller is my choice,, Im 56 & Ive had mine since I was 22,, & its been used,, a lot.
Youve got the right amount of solder when the wire is silvery but you can still see the shape of the individual strands in each wire.
A glob aint doin the best job.
Its plenty okay if the solder stops before the wire gets to the insulation.Better, in fact. Solder will run, where the flux melts to.

My experience is that those crimp connectors work, & May work for years,, or not,,

If the original lites have the mating bullet connections on them, cut them off & solder them onto the new lites,, then, its connections as good as factory, cuz they ARE the faktree connections.