I just use a Network cable tester to test my RJ45 network cables. Network RJ45 cable testers are also very easy to use. All you have to do is plug in both ends of the cable in to the network cable tester, and the network cable tester tests if the cable is broken or damage by sending a small current through it. If the cable is broken, it usually makes a sound or turns on a visual warning like a light. The network cable tester runs on a 9V battery.
I like using a rechargeable 9 Volt battery since it is more environmentally friendly, and cheaper in the long run.
It is also a good idea to have a network cable since sometimes you need to connect your laptop, or PC to a router or switch to make changes to the control panel inside the router or switch, or to test if the network cable tester is working properly.
Another tool you will need is a RJ 45 loop back plug for your RJ45 network card to see if it is your cable, hub, router, switch or network card which is broken.
If you have networking wire, and the network plugs, you can make one yourself by following tutorials on "how to make a loopback plug" by searching on the internet. You also need a Network wire Crimper to put it all together. Loopback plugs are good for using the command prompt to run ping localhost or ping 127.0.0.1 if Domain Name Service is down.
A network crimper and network wiring plugs will also come in handy for repairing broken network cables.
To learn how to use these networking tools, you will need a good book on networking troubleshooting and management. I read Mike Meyers Comptia Network+ All-in-One certification textbook. It is a great text book for learning how to troubleshoot, manage, and repair your home wired and wireless network. I like how there are so many pictures, diagrams, and tables for explaining all the different terminology and tasks to keep a home network running well and secure. It also comes with a CD with exam questions for the Network+ exam.
Trouble shooting a wireless network is not really hard, so you usually don't need any tools for troubleshooting wi-fi wireless networks in my experience. If you can connect to another unsecured wireless network with your laptop or PC. Most likely your wi-fi router is broken, you need to turn on wifi for your router, or needs to be restarted. If only your computer or laptop can't connect to the wi-fi network and your friends laptops can, most likely your wi-fi adapter can't connect to a WPA or WPA2 connected wi-fi signal, or you typed in the SSID, password for the wi-fi in wrong. The network administrator or you also might of typed in your MAC address in wrong if your router is using MAC filter. You might need a new Wi-fi USB adapter or router if either are broken.