I am sure there is an obvious answer to this question, so I apologise in advance. I ordered some matrix board, but what arrived has no solder pads. Every matrix board I have used has the solder pads, and so I am not sure what to do. The board has the holes, just no pads... Is this board for a different purpose?, or is there a way to solder circuit components to this board?
You got bare perf board without pads, by the sound of it.
Yes, you can use that to make prototypes, just solder thin insulated or bare wires (think wire-wrap wire or something like AWG30 solder-through magnet wire) to the pins of the devices.
It's even possible to use it for SMT devices if you glue them down with legs in the air dead-bug style.
Probably it's not a matrix board, but just a plain board. This means you can yourself solder lines as you seem fit. This way you do not have to stick to the 5x5 or 10x10 (or other) predefined solder pads.
Or if you need bigger distances (more than a few holes apart), to use wire with isolation (like breadboad/dupont kind of cable).
If you mean the solder pads on one or two sides missing, than an alternative is to use so-called PCB terminal (block)s like below. They come in different sizes (mostly 2 to 8 wide).