Git - How do I just switch to and pull the changes from another branch? All locally

So I’m having problems with git since it’s needlessly complicated, literally the only thing I want to do, is, let’s say, switch from master to a newer or older branch and pull the changes to my local machine, that’s it. I’ve tried doing

git checkout <branchname>

git fetch

git pull

but it doesn’t download any changes from the branch I switched to. How do I do it properly? I don’t want to upload anything to the actual repository, no commits or merges to master etc., I just need to switch branches for testing purposes, being able to run it locally.