There are a number of tools for controlling custom normals. Any tool that adjusts custom normals requires that autosmooth be enabled. I recommend setting autosmooth angle to 180 when messing about with custom normals, as there are circumstances where Blender can create custom normals for only some verts, leading to autosmoothing other verts.
While there are a number of ways to individually tune normals, I don't find that useful. It's too easy to screw things up, and you can easily have too many normals to be able to meaningfully tune. Thankfully, there are a lot of other great tools you can use to modify normals en masse.
Your first tool is a normal edit modifier, which can let you create custom normals from the position of some other object-- either radially from the position of that object, or parallel directional normals, from the origin to the object. These are useful for creating simple spherical or flat normals. You can tune the mix factor and limit with a vertex group. You can apply the modifier to write the custom normals, or leave the modifier live.
For more complicated normals, I'll generally use a data transfer modifier that copies the normals that I want from some other object. This lets me tune normals exactly how I want, but through the use of all of the mesh tools with which I'm familiar; I can easily visualize the normals, and with reasonable choices, I'll always get continuous, reasonable normals (unlike manually editing normals):
For this kind of task, nearest face interpolated is my preferred mapping. Again, I can limit with a vertex group; I can apply or leave live.
Note that if the goal is use in a different renderer, you need to apply, and while live custom normals can fix a lot of topo problems, applied custom normals can't. However, it is relatively easy to recreate most live custom normals in a game engine shader if needed.
Sometimes I'll do a data transfer of normals, by topology, from a copy of the mesh:
Left to right: base Suzanne, Suzanne with data transferred normals, mesh edited Suzanne used as target of data transfer.
This is pretty much the nuke level of normal editing. I can create any normals I want, I can use any mesh editing tool I can dream up to create those normals, and I'm guaranteed smooth, mesh-appropriate normals.