How can an attacker use a compromised computer to do things over the internet? For example, if an attacker infects a PC with a general payload, other than searching through the computers files and changing things, what else can they do? For instance, can an attacker use a compromised computer to surf the internet? If so how is this done in general terms? If they have a reverse shell open or whatnot, you cannot really see webpages and so forth, so do they somehow push their activity through the compromised PC? If so what do they need to do this?
They can do a heck of a lot
One of the most common misconceptions I hear people say about cyber security is, "Well, hackers have no reason to come after me/this." As long as you have some type of connection to the internet, hackers have plenty of uses for your hardware. It does not matter if you are running a high-end server or a smart refrigerator, your system is worth something to a hacker.
Things you can do from just about any hacked device
DDoS attacks: A hacker with access to a large number of compromised devices, organised into something called a botnet, can use them to all simultaneously access an internet resource to try to overwhelm its capacity. This requires they install a very simple program on your device.
Brute Force Attacks: Many systems lock you (your IP address) out after so many password guesses. If you get locked out after 10 guesses, then you can only get into a system if it uses one of the 10 most popular passwords before you have to wait and try again later. If you have a botnet of 100 compromised devices to work with, then you get 1000 guesses before you are locked out. This also requires they install a very simple program on your device.
Spam: Servers that send out spam are routinely flagged and blacklisted, but if you have a lot of hacked computers to work with, you can use them each as spam platforms so when one gets blacklisted, you move on to the next. This could either rely on installing an SMTP Virtual Server on your device or just hacking your personal email account using spyware to use as a spam platform.
- Targeted Spam: Again, using spyware, they can send spam from your personal account, but they can specifically target your contacts to take advantage of the trust people have in knowing you personally.
Proxying (out to the internet): They can set your device up as a proxy for their own (often illegal) online activities. Basically they just need to install VPN endpoint software on your device, and all of their traffic will be routed through your IP. As long as they control your device well enough to make sure it is not logging their access to it, they can make it look like you are the one doing the illegal activity, and not them.
Proxying (into a local network): Another application for using you as a proxy is to gain access to local network resources. If your device is on a local network, it may have access to Servers, NASs, Security Cameras, etc. that can not be directly accessed from the internet. But by proxying through a device that can access both the internet and your LAN you can use it to attack systems that would otherwise be inaccessible from the outside.
Things where something more powerful like a PC or Laptop are preferred
Crypto Mining: Mining things like bitcoin uses up a lot of electricity and processing power and can burn out components quicker. By using a hacked computer to do this, they don't have to pay the costs for all that, you do. They just need to install crypto mining software on your machine and attach it to a wallet they control.
File Storage/Hosting: They could use your computer as a file repository or web server; so, if they need somewhere to store a bunch of pirated media or to host their child pornography website, they could create a hidden partition or virtual machine on your computer to do it.
RMM: An even more extreme form of using you as a proxy is to take total control of your machine and use it as though it is their own. Windows has built into it a thing called Remote Desktop Manager which allows Windows to share its desktop over the internet. Mac and Linux also have easily installed counterparts that do the same thing. There are also some RMM programs you can install that can give you a full desktop view of a machine that is separate from what the end user can see so you do things without being noticed. If a hacker puts RMM software on your computer, then they can use your computer in every respect as if it were their own. This would make implementing any of the previous uses much easier, or they could just use it in whatever personal ways they prefer. It could even be something as ridiculous as using it to run an instance of Minecraft with a wiggle script so that they can idle farm cactuses with a zombie account while they do their real playing on their personal computer.