Yes, you can run homebrew launcher using a couple of different methods. It's all explained here:
http://smealum.github.io/3ds/
Homebrew launcher lets you run user created code. You can NOT run roms with homebrew. You CAN run emulators, user tools, out of region games, and custom themes.
If you want to run roms. You'll need a kernel exploit which is only available on firmware 9.2, so you'll have to downgrade from 9.7 to 9.2 then install a CFW
Before you do that though, make sure you know what 3DS you have. shoutout to legofan623 for providing that link above.
Here is a guide to downgrading:
http://www.modzlink.com/3ds-106-to-92-downgrade
Here is a guide to which CFW you should use:
http://hackinformer.com/2015/07/03/beginners-guide-cfw-3ds/
From there you'll need to install the CFW of your choice. I recommend reiNAND on New 3DS (or New XL) and rxTools for Old 3DS (or 2DS, or XL)
There is a nice video guide by Mr.Mario2011 for both options. You'll have to remove the spaces between youtube and .com since it wouldn't post correctly for some reason.
New 3DS with ReiNAND:
https://www.youtube .com/watch?v=pJezO56ILjY
Old 3DS with rxTools:
https://www.youtube .com/watch?v=x9ZMJXGtYos
Also look into reading this to understand the difference of emuNAND and sysNAND and how each one works:
https://gbatemp.net/threads/guide-a-noobnands-guide-to-sysnand-and-emunand.410439/
I would stop after that and get used to the 3ds modding community before getting into the more complicated Arm9LoaderHAX because the brick risk is higher and I wouldn't recommend without being familiar with 3DS modding.
Happy modding