And even on the deep web, you don't 'stumble' on such things. You have to look for that sh*t. On the deep web, you have to look for everything, it's the principle of it being deep. Of course, you can find strange, and even absolutely illegal stuff on it, but the main part of the 'deep' web isn't child porn, drugs, hitmen, or weapon dealing. It's just basically any server that is not dedicated to web services.

Game servers are in the 'deep web', FTP servers are in the 'deep web', if you have a server at home that is not referenced on any DNS, that's a part of the deep web. Even user computers are part of the deep web.

What is not in the deep web, is basically any service that is unreferenced, and as such, can only be accessed through the IP address. That's why it's 90% of the internet, think of all the multiplayer games there are, that alone must be 45% of the internet (just a guess here).

To access it, download tor. Tor is a browser and a network that hides your real IP address, so that no-one will trace it back to you. Think of yourself being a tree in the forest, no one will know if you're doing something illegal if they don't know where or who you are. Tor is used by darknet users, but also by some others, because it hides your IP, it provides a "shield" if you want to illegally download stuff, access restricted websites because of your area, shit of the sort. You may take the IP address of someone in the USA while you live in China, for instance, which allows you to watch USA-onlly web pages and videos.

TL;DR: Even on the deep web, you will be able to find anything if you look for it, you won't stumble accidentally onto CP, guns, or drugs. And the illegal part of the deep web, is just a tiny fraction of it, because of the definition that is not in the deep web.