There's a million tutorials out there how to learn git. This isn't one of them. I'm going to assume that you learned git a while ago, you've been using it a bit and you're generally familiar with its principles. I'm going to show is a couple of things that improved my workflow. Chances are, it will improve yours too. This isn't a tutorial though. I'm just pointing you in the direction of things, you'll have to learn how to use them yourself.
Use tig
Seriously. Don't tell me you use gitk or git log is good enough for you. Use tig. tig is to git log what mutt is to mail(1). It has been the source of the biggest efficiency increase for me. Screenshots don't do it justice because the selling point is that it is interactive. But anyway, here are some official screenshots: tig blame shows you the file and the commits, you just need to select the line, hit enter and you see the actual commit. The main view by default shows you tags, branch names, remote branch names, etc. So not only do you immediately know which branch you're on, you will see local branches that have been merged, tags that have been applied, etc. It gives you an awareness that git log doesn't. Do yourself a favour, install it, use it for a day or two and I'm pretty sure you won't go back.
tig also supports custom configurations. Here is my $HOME/.tigrc:
bind generic X !git cherry-pick -x %(commit)
bind generic C !git cherry-pick %(commit)
bind generic R !git revert %(commit)
bind generic E !git format-patch -1 %(commit)
bind generic 0 !git checkout %(commit)
bind generic 9 !git checkout %(commit)~
bind generic A !git commit --amend -s
bind generic S !git show %(commit)
So with a couple of key strokes I can cherry-pick, export patches, revert, check out a single tree, etc. Especially cherry-picking is extremely efficient: check out the target branch, run "tig master", then simply select each commit, it "C" or "X" and done.
Use branches
Anytime it takes you more than 5 minutes to fix an issue, create a new branch. I'm getting torn between multiple things all the time. I may spend a day or two on one bug, then it's back to another, unrelated issue. With the review requirements on some projects I may have multiple patches waiting for feedback, but I can't push them yet. Hence - a branch for each feature/bugfix. master is reserved for patches that can be pushed immediately.
This approach becomes particularly useful for fixes that may need some extra refacturing. You start on a feature-based branch, but halfway through realise you need a few extra patches to refactor things. Those are easy to review so you send them out to gather reviews, then cherry-pick them to master and push. Back to your feature branch, rebase and you're done - you've managed two separate streams of fixes without interference. And most importantly, you got rid of a few patches that you'd otherwise have to carry in your feature branch.
Of course, it takes a while to get used this and it takes discipline. It took me a few times before I really managed to always work like this but the general rule for me is now: if I'm hacking on the master branch, something is off.
Remember: there's no real limit to how many branches you can create - just make sure you clean them up when you're done to keep things easy for your brain.
Use the branch names to help you. You can rename branches (git branch -m), so I tend to name anything that's a bigger rewrite with "wip/somefeature" whereas normal bug fixes go on branches with normal names. And because I rebase local feature branches it doesn't matter what I name them anyway, the branches are deleted once I merge them. Branches where I do care about the branch history (i.e. those I pull them into master with a merge commit) I rename before pulling to get rid of the "wip" prefix.
Use branch descriptions
Hands up if you have a "devel" branch from 4 months ago. Hands up if you still remember what the purpose of that branch was. Right, I didn't think so. git branch --edit-description fires up an editor and lets you add a description for the branch. Sometimes a single sentence is enough to refresh your memory. Most importantly: when you task-switch to a different feature, edit the description to note where you left off, what the plan was, etc. This reduces the time to get back to work. git config branch.<branchname>.description shows you the description for the matching branch.
I even have a git hook to nag me when I check out a branch without a description. Note that branch descriptions are local only, they are not pushed to the remote.
Amend and rebase until the cows come home
The general rule: what is committed, doesn't get lost. At least not easily, it is still in the git reflog. So commit when you think you're done. Then review, test, add, and git commit --amend. That typo you made in line 4 - edit and amend. I have shell aliases for amend, rbs (git rebase -i) and rbc (git rebase --continue), and almost every commit goes through at least 3 amends (usually one because I missed something, one for that typo, one for commit log message editing). Importantly: it doesn't matter how often you amend. Really. This is local only, no-one cares. The important thing is that you get to a good patch set, not that you get there with one commit.
git commit --amend only modifies the last commit, to go back and edit the past, you need to rebase. So, you need to
Learn how to rebase
Not just the normal git rebase, the tutorials cover that. Make sure you know how to use git rebase --interactive. Make sure you know how to change the ordering of a commit, how to delete commits, how to abort a rebase. Make sure you know how to squash two commits together and what the difference is between squash and fixup. I'm not going to write a tutorial on that, because you can find the documentation is easy enough to find. Simply take this as a hint that the time you spend learning how to rebase pays off. Also, you may find git squash interesting.
And remember: even if a rebase goes bad, the previous state is still in the reflog. Which brings me to:
Learn how to use the reflog
The git reflog is the list of changes in reverse chronological order of how they were applied to the repository, regardless what branch you're on. So HEAD@{0} is always "whatever we have now", HEAD@{1} is always "the repository before the last command". This doesn't just mean commits, it remembers any change. So if you switch from branch A to branch B, commit something, then switch to branch C, HEAD@{3} is A. git reflog helpfully annotates everything with the type, so you know what actually happened. So for example, if you accidentally dropped a patch during a rebase, you can look at the reflog, figure out when the rebase started. Then you either reset to that commit, or you just tig it and cherry-pick the missing commits back onto the current branch. Create yourself up with a test git repository and learn how to do exactly that now, it'll save you some time in the future.
Note that the reflog is local only. And remember, if it hasn't been committed, it's not in the reflog.
Use a git push hook
Repeat after me: echo make > .git/hooks/pre-push. And no more embarrassment for pushing patches that don't compile. I've made that mistake too many times, so now I even use my own git patch-set command that will run a hook for me when I'm generating a patch set to send to a list. You might want to make the hooks executable btw.