It's very easy. You should make sure that automatic downloading of new firmware is disabled in the Settings.
Then you visit
https://henkaku.xyz/ (use this domain, there is a fake site on a very similar domain that uses the very same design. .xyz is the right one.) on your Vita and press the install button.
The installation can throw a error and fail multiple times (likely it will do it) just retry it a couple of times. It works. The reason for this is that the hack uses a such called
race condition (a bug in the rendering engine that the browser uses).
After that you start the new program ModecularShell on your Vita (it will be installed as a new bubble) and press the select button in the shell.
Now you can use the shown IP/port in a FTP program as FileZilla to transfer .vpk files (that's the file extension for installer used by ModecularShell).
Copy only to ux0: (and subfolders) that is your memorycard (or internal storage if you haven't inserted a memorycard and it's a Vita 2000/slim model).
I made me a folder called henkakuUpload, maybe you want something like this too.
Also it's good to know that all data from homebrew should be installed to ux0:/data/[folderCreatedByHomebrew] (some homebrew breaks with thos convention...)
Games and homebrew are always provided as .vpk (or as source code).
You have to install HENkaku everytime you reboot your Vita. Therefore I recommand to install the offlineInstaller (you can find a link to it
here, feel free to go through the whole list of homebrew. It includes e.g. some nice emulators (there is also a PSX emulator not listed there yet as part of the RetroArch nigthlies)).
If you need further explanation of one of this points feel free to ask.
Personaly I recommand to logout from PSN (not unregister your Vita from the account, just logout) first, even if you can use the PSN (including the store) on 3.60 while HENkaku is installed atm (that's called PSN spoofing).
It's important to know that HENkaku has to be installed to run games/homebrew you installed with a vpk (you can delete the vpk once you used it).
Edit: If your Vita downloads a new version of HENkaku once you install it again after a reboot (there will be a progress bars as by the first installation) you should check out the
changelog 
