noob question about connecting components

Is there a convenient way to connect three stepper motor driver (which each take up 4 I/O pins) on the Arduino, while using the same battery for all of them?
The motors are 28BYJ-48 stepper motors.

Stepper motor drivers typically use 2 pins per motor, for step and direction. The motor power supply goes to the driver boards.

Do I need to have a wire going through the driver boards, attaching them? Like attaching the negative on one to the positive on the next? If so, where do the ones at the ends meet up to on the Arduino?

You connect the driver boards in parallel, all negatives to negatives and all positives to positives. The power supply goes to the driver boards. The negatives also connect to the Arduino Gnd.

The only power supply I have is a 9V battery, which I'm using this connecter thingy to go directly into the built in arduino battery plug. Is there a way for me to connect it from the Arduino to the drivers, using that?

You can connect the battery also to the Arduino, but most probably a 9V battery can not power even a single stepper motor. It's already a bad choice for powering only an Arudoino.

Do I need to solder something?

I’m sorry but I don’t think I’m good enough with Arduino to work this out so easily. If you could list out the connections I need between each component- or do a sketch thing- that’d help me to visualize it.

Get an Arduino Starter Kit and you get all the detailed instructions you need.