How can a rooted Android phone generally get bricked? I've rooted my phone but now I'm scared that it would be bricked. I've seen a page on "Tips to prevent from bricking" and it said to install custom ROM recovery or something like that. I think there were two things; ClockWorkMod and Team Win.

I tried to install one and downloaded ROM manager but didn't work (didn't find my device model name).

Doing what kind of things increases the probability of bricking my device?
Doing exactly what you are doing is probably the biggest chance of bricking your phone - experimenting without proper knowledge and understanding of how things work. Go into xda-developers and find your phone's forum. Then start reading - how to install a ROM and a Recovery, change kernels etc. Read the threads and follow the steps exactly as they are shown and you won't be having any problems. All it takes is for you to mess up a single step, to brick your phone - may it be you download wrong file, not for your model or you type in wrong command etc. Still Android these days (not like back in 2010 for example) are quite resilient. It's not too difficult to recover from almost all kinds of bricks. 

TLDR Read how other people did it before you on accredited sites like XDA-Developers and be careful.

Story time: I've been doing this (rooting, installing roms etc. - being power user)  for 5-6 years now so I know my stuff. I started unlocking my LG G4, then rooting, then installing recovery. What I did here was really stupid. Instead of installing a recovery I booted into it - so I had access to it only once. But I didn't notice right away. I installed my files, and the installer required a restart, and to boot back into recovery. But since I didn't install recovery the first time, as soon as I restarted my phone I literally messed up. I went into semi-soft brick. No access to fastboot, couldn't hook up my phone to my PC to execute commands, and the phone was in bootloop, only going as far as the logo.
Well I panicked a bit, went into the forum and started reading for solutions. At the end, something written for totally different thing allowed me to push some commands, and salvage my phone. 

Also on your comment: And in general, don't root if you don't know what it is. Many people do root exactly for your reasons "people say its cool" I rooted to install xposed and get some modules I need.