I have 2 server at which I am working locally. The first is a front-end in Vuejs, and the second is back-end in Flask. From the client I request an api to the second.
I have to upload these two on a remote Linux VM (Debian), for which I have credentials and I can successfully connect it via PuTTy.
How do I transer my 2 directories to the VM?
Then, I should change the address that the client uses for api requests of the server, that is all? Or I will have to do something else?
You can copy directories by the scp or sftp protocol. In your case, this can be done most easily by the winscp software.
Both scp, sftp (implemented by winscp) and ssh (implemented by putty) use the ssh protocol. Putty is for remote terminal (i.e. you can give commands to the server), while winscp uploads, downloads and manages files on it.
If you are developing something, it is likely that you will need to this deployment more regularly. These softwares are only good for single-time deployments. In professional environments this deployment is automatized and happens quickly.
It is very likely that you also have some database in your project. Here the most common options are either some db-level synchronization, or dumping the database into files and synchronizyng on the file level. But it is already another topic.
It is also unlikely that you will need two different VMs for the vuejs and for the flask. You could wire them together to a single VM, that would make your task far more easy.
You will likely have a hard time to make your deployment on your server well working. This all is just the beginning. But don't worry, after you've learnt it all, it will be easy!