First of all, you should use a higher resolution for your mesh; you can always decimate it later. Then you should have Dynamic Topology toggled on. This will generate new mesh while sculpting instead of using only the existing mesh. From the Dyntopo dropdown choose a nice detail size.
Here are some basic brushes for generic sculpting:
Draw: simply adds more volume.
Crease: sharpens and deepens a specific area.
Smooth: the opposite of crease.
Snake Hook: pull and twist.
Grab: quick and nice way to adjust an area.
If you want pierced holes in your model, you will have to use a boolean modifier (difference) with an object to dig the hole (like a cylinder). As far as I know, you cannot pierce a mesh in sculpting mode. Digging into a hole in sculpting mode will only push the other side out.
As for filling holes (pierced or not), just use the Draw brush. If your model is not symmetrical, then disable the brush mirroring.
Unfortunately upping the Dynotopo resolution just made it more of a mess…
Thank you StrayBillie, that helped. I was able to uncluster the vertices to point where I was able to clean it up somewhat. Not perfectly, but enough for a high resolution remesh to clean up the remaining problems. Thanks!
You need to tweak the resolution of Dynotopo from the dropdown. And the mesh you show in the pictures can be fixed/smoothed with the Smooth tool.
Dyntopo is very useful sometimes when you don’t want your mesh simply to be stretched, but add more detail. Even if it doesn’t suit your needs at the moment you shouldn’t underestimate it.
Dynamic topology (aka dyntopo) is a dynamic tessellation sculpting method, adds and removes details on-the-fly, whereas regular sculpting only affects the shape of a mesh.