First...get that grass out of there and check the depth of the tree. Looks like it may be too deep (a common problem), but we can't tell with all of the grass.
If it were mine, I'd remove whole stems - ideally down to a single trunk. That will be a much stronger tree in the long-term. If I am not allowed to go down to 1 trunk, I'd at the very least get rid of that crooked one on the right, the shortest one on the left and the short one that is kinda just right of center as we look at that picture. that would clean it up quite a bit.
The next step is finding branches that are disproportionately large to the trunk. If the branch is more than 1/3 to 1/2 of the diameter of the trunk, it needs to be reduced or removed.
Now look at the top of each trunk that remains...if there is not just a single leader prune back co-dominates.
Finally, if there are just a few lower branches that look out of place prune those off.
Make sure you are making good pruning cuts with a sharp saw or pruners.