How can I deploy my Rails apps anywhere in the world (including my shared hosting http://www.moxo.cz/)? I tried Heroku, but I had problem with moving my dev db. Then I found mod_rails and it seems I can finally put my app on mydomain.net/railsapp but it's probably impossible to deploy on shared hostings. If I built Rails app for my client how would I deploy it on his "plain" hosting or anywhere else? I have no experience with that and it's getting desperate.
Heroku is a very easy option. In a plain server you usually have a ruby stack preinstalled, your provider should provide documentation about it, if you don't have a stack preinstalled you will have to install all stack yourself which is a lot of effort.
I would recommend you to try again Heroku, you could post your problem here in SO.
mod_rails is a plugin also easy to use when you have al the stack preinstalled and preconfigured. EC2 is a good option for this. Although is not as simple is this is written, you have to find and use a preconfigured stack which usually is not a problem.
I suppose you have a provider in mind, but this is the general flow.