Say I have some idea about research and I want to suggest it to a potential collaborator (researcher). Assume that I don’t know the researcher personally and have no any ties with him. If I write my idea to him, there is a threat that he will steal it and proceed without me, right? Is there a way to do this in a way that both me and the potential collaborator do not enter that risk?
You are correct that it MIGHT be the case that another researcher uses your idea without acknowledging you. However, the chances are much higher that your idea is not even good enough that the other researcher wants to collaborate with you. Keep in mind that the other researcher is probably an expert in his field and might either think this idea is trivial or is not realizable due to problems you are not aware of now. I do not want to demotivate you, but in my experience "That is the best idea ever. I am going to steal it and get famous" is the least probable reaction.
So to answer your question about how to continue: Your main task is to convince the researcher that your idea is worth the effort. It is much better if you already have something to show, some preliminary results or a simulation that shows your idea might work out. That is the best point in time where you can contact another researcher and ask if you can collaborate to refine the work and publish it. If you fear that the other researcher might steal your idea, you could also publish your preliminary work at arXiv. Think about why you want to collaborate and why you can not realize it on your own.
I do not fully understand his work and I hope he can explain to me how my idea can be realized with his methods: Chances are very high that your idea does not work out. Try hard to understand his work first. If you have questions, you can try to ask, but do not expect that the other researcher will teach you all the basics just because you might have an idea.
I do not have the time to realize it and just want to share the idea: The other researcher probably has no time either. Sharing is great, but do not expect much from the collaboration.
I know how to realize it, but I do not have the equipment: That is a very reasonable cause, but then try to do some calculations or simulations that show that your idea might work.
I can only realize parts of the work. For example I can do the implementation of an algorithm, but I am not able to prove that it works for all corner cases: Very reasonable, nobody is an expert for everything. But then at least begin with your part and show how it works before contacting a potential collaborator.
I just want to have his name on my paper: Please don't!