I find merge tools rarely help me understand the conflict or the resolution. I'm usually more successful looking at the conflict markers in a text editor and using git log as a supplement.
Here are a few tips:
The best thing I have found is to use the "diff3" merge conflict style:
git config merge.conflictstyle diff3
This produces conflict markers like this:
<<<<<<< Changes made on the branch that is being merged into. In most cases, this is the branch that I have currently checked out (i.e. HEAD). ||||||| The common ancestor version. ======= Changes made on the branch that is being merged in. This is often a feature/topic branch. >>>>>>>
The middle section is what the common ancestor looked like. This is useful because you can compare it to the top and bottom versions to get a better sense of what was changed on each branch, which gives you a better idea for what the purpose of each change was.
If the conflict is only a few lines, this generally makes the conflict very obvious. (Knowing how to fix a conflict is very different; you need to be aware of what other people are working on. If you're confused, it's probably best to just call that person into your room so they can see what you're looking at.)
If the conflict is longer, then I will cut and paste each of the three sections into three separate files, such as "mine", "common" and "theirs".
Then I can run the following commands to see the two diff hunks that caused the conflict:
diff common mine diff common theirs
This is not the same as using a merge tool, since a merge tool will include all of the non-conflicting diff hunks too. I find that to be distracting.
Somebody already mentioned this, but understanding the intention behind each diff hunk is generally very helpful for understanding where a conflict came from and how to handle it.
git log --merge -p <name of file>
This shows all of the commits that touched that file in between the common ancestor and the two heads you are merging. (So it doesn't include commits that already exist in both branches before merging.) This helps you ignore diff hunks that clearly are not a factor in your current conflict.
Verify your changes with automated tools.
If you have automated tests, run those. If you have a lint, run that. If it's a buildable project, then build it before you commit, etc. In all cases, you need to do a bit of testing to make sure your changes didn't break anything. (Heck, even a merge without conflicts can break working code.)
Plan ahead; communicate with co-workers.
Planning ahead and being aware of what others are working on can help prevent merge conflicts and/or help resolve them earlier -- while the details are still fresh in mind.
For example, if you know that you and another person are both working on different refactoring that will both affect the same set of files, you should talk to each other ahead of time and get a better sense for what types of changes each of you is making. You might save considerable time and effort if you conduct your planned changes serially rather than in parallel.
For major refactorings that cut across a large swath of code, you should strongly consider working serially: everybody stops working on that area of the code while one person performs the complete refactoring.
If you can't work serially (due to time pressure, maybe), then communicating about expected merge conflicts at least helps you solve the problems sooner while the details are still fresh in mind. For example, if a co-worker is making a disruptive series of commits over the course of a one-week period, you may choose to merge/rebase on that co-workers branch once or twice each day during that week. That way, if you do find merge/rebase conflicts, you can solve them more quickly than if you wait a few weeks to merge everything together in one big lump.
If you're unsure of a merge, don't force it.
Merging can feel overwhelming, especially when there are a lot of conflicting files and the conflict markers cover hundreds of lines. Often times when estimating software projects we don't include enough time for overhead items like handling a gnarly merge, so it feels like a real drag to spend several hours dissecting each conflict.
In the long run, planning ahead and being aware of what others are working on are the best tools for anticipating merge conflicts and prepare yourself to resolve them correctly in less time.