I moved to Europe from the USA, so I had your problem. Electronic equipment comes in a variety of flavors, but most can be adapted to both 115V/60Hz and 230V/50Hz, because it is easier and cheaper for a manufacturer to use the same bill of materials for all regions of the world. Here are the different varieties you will encounter:
- Autosensing: You just use the proper cord, and everything works. Generally this is the case for a lot of equipment with SMPS power supplies. Swap out your NEMA (USA) plug / C13 cord for a Schuko (Europe) plug / C13 cord.
- Switchable: These types of equipment have a switch, typically located near the IEC inlet, mostly on the outside of the equipment, but sometimes on the inside (check the manual). With the equipment off, slide the switch to the proper voltage. Be careful to not plug it into the wrong mains voltage! Use the proper power cable,
- Internal jumper: Sometimes you need to replace an internal jumper with a different one. If your equipment is not autosensing or switchable, try contacting the manufacturer and see if they have a different jumper. If you change the jumper, label the equipment on the outside so you know what voltage it takes. Use the proper power cable.
- Rewire-capable: A manufacturer will often use a transformer with the capability to handle both voltages (typically the primary winding is divided into two parts that can be wired in series or in parallel, depending on input voltage). If they don't use an internal jumper, you can rewire the transformer. Do not do this unless you know what you are doing! You need to know the transformer wiring, and often, you will need to know how to solder properly (if you have not soldered thick, heavy terminals, it's different than soldering thin wires). Label the equipment on the outside so you know what voltage it takes. Use the proper power cable.
In many of these you may need to change the fuse to a different value (fuses are based on amps, and when using twice the voltage you use half the amps). Check with the manufacturer -- some recommend fuse changes, some don't.
I was fortunate enough to be doing a system upgrade while knowing I was going to move, with enough lead time to check the details of equipment before purchasing. I encountered equipment in each of the four categories above. Everything works fine here in Europe.

