A plastic gear of an older DVD player broke. I always read about being 3D printing a "repair revolution". So I looked for a template to give to some printing service, but I found none (and nothing close to it).
Could you please explain me, what steps a layman should take to get the gear piece replaced using 3D printing?
If you have the remaining pieces of the gear and enough remains to determine certain measurements, one can either engineer the gear using a number of gear modeling designs, or one can take measurements directly from the parts and engineer a raw design.
If the gear you have is not particularly peculiar, it is possible to use a gear generator plug-in, template, or library to make the "foundation" of your gear. The modeling software would then be used to add the appropriate bosses and key ways required to complete the design.
If you are considering to create the part yourself, you have a wide selection of programs from which to choose. I'm fond of OpenSCAD, and it does have a number of gear libraries. Simple bosses and key ways are easily accomplished using OpenSCAD.
Another package available on the internet which includes the option of using a gear generator is Tinkercad which has a reputation of being easy to use. You'll find many tutorials for this program as well.
Tinkercad requires an "outside" program to generate the gear design which is then imported to the model workspace. Even a program as simple as Inkscape can create gear profiles to be imported into many design packages.
Fusion360 is available free for hobby or non-commercial use, but may not be the easiest to learn in a short time.
So many others as well. Use your favorite search engine for "gear generator modeling software" or similar wording and be overloaded with links.
This is not something "a layman" can do. If you want to replace that gear using 3D printing, you'll either need to go down the rabbit hole and learn a bunch of new skills, or hire someone to do it for you.
You need to have a 3D model of the part you want to replace. While 3D scanning is in some cases possible, it won't give you the resolution required to reproduce the gear with sufficient accuracy. This means your only option is to manually model the gear in CAD software. You'll need to take a bunch of measurements (outer and pitch diameter, thickness, mounting hole diameter) and figure out the tooth profile, and then build a model according to those measurements. A caliper is very helpful when doing this.
A neat trick that might help with a flat part like a gear is to scan it on a flatbed scanner, and then use the resulting photo to trace your CAD sketch over (but you'd still need to cross-reference it with measurements).
Unfortunately, most CAD software is quite complicated and "How do I model a gear" is not a question that can be answered concisely. @fred_dot_u offers a number of suggestions for packages that might work, and even offer modules specific to generating gears. However, if you are not interested in learning CAD for its own sake and really get into 3D printing, learning it just for the sake of replacing a gear in a DVD player is a very inefficient use of your time.
The only 'layman's' option is to find an existing design which solves your problem. If you are lucky, and the product you have has a common failure mode, someone else might have a) solved the same problem already, and b) posted their design online.
Sites such as thingiverse have plenty of designs, but finding the right thing might be hard. If you find something, you can then look for someone to print it for you. Its not clear if you tried this already, but maybe the answer helps someone else.
