I suggest you not to upload them just in Colab, since when you’re restarting the runtime you will lose them (just need to re-upload them, but it can be an issue with slow connections).
I suggest you to use the google.colab package to manage files and folders in Colab. Just upload everything you need to your google drive, then import:
from google.colab import drive
drive.mount('/content/gdrive')
In this way, you just need to login to your google account through google authentication API, and you can use files/folders as if they were uploaded on Colab.
EDIT May 2022:
As pointed out in the comments, using Google Drive as storage for a large number of files to train a model is painfully slow, as described here: Google Colab is very slow compared to my PC. The better solution in this case is to zip the files, upload them to colab and then unzip them using
!unzip file.zip
More unzip options here: https://linux.die.net/man/1/unzip