3D modeling is a broad subject. So broad, in fact, that in industry there are multiple sub-disciplines that focus on just one part of making characters (i.e. people who make the mesh, people who do the rigging, and animators who create animations).
I have made, rigged, and animated my own characters from scratch before, but would not dare call myself an expert or even competent. Take that into account when you read this answer.
For creating meshes, you’d use 3D modeling software. There are plenty of programs to choose from, but unless you’re made of money, you should probably choose Blender as it is free, open source, and has plenty of teaching materials that are available (even if most of it is presented in the form of videos, which is unfortunate but understandable.)
Modeling works best if you have reference images to work with. i.e. one front and one side-facing picture of your character, both in the same pose and presented at the same scale. For humanoids you’d probably want a T or an A pose. If your robot isn’t humanoid, then you should figure out the rest position for yourself.
Rigging in Blender can be done from scratch by building an armature bone by bone, or if your character is humanoid, by using Rigify. Animation with Rigify armatures can result in mesh stretching, which is less than ideal when importing the mesh into Godot. Ideally, you only want to export deformation bones. To do that, you can use the Rigodotify add-on for Rigify.
Breaking up the character into submeshes may or may not be a good decision based on the overall mesh. Rigify tends not to work very well if your mesh has intersecting geometry, so if you have that, splitting into parts can be a good idea.
A special consideration in your case is that robots tend to have little in the way of flesh. In your case, rigging will probably consist of assigning 100% weights to specific bones in vertex groups.
I haven’t tried making animations in Godot itself, but I understand that’s possible. What I do is make animations in Blender, animate there, then export them. If you export as a GLTF/GLB, you can attach a Skeleton3D and attach modifiers that let your character hold other meshes (e.g. a weapon) or set up IK.
It took me literal months to make my first character from scratch, rig, texture, and animate her. And then I had to completely redo parts when I learned more about hair works. (Pro-tip: do not give your robot any hair.) Expect lots of searching on the internet, quite a bit of fiddling, and maybe a few dead ends. But if you’re patient, it should all work out in the end.
