If you want to backup files online, then it is a good idea to keep them encrypted. Of course, the storage space provider is trying its best to keep them safe, but in case of human error, technical deficiency or fraud your files might be surfing the internet being a very unpleasant issue, even if the data is not confidential.
The first way is to encrypt the directory structure with all files in it one by one. That is a recursive directory encryption which might be combined with file name obfuscation (maybe something like gpgdir, read also Ben Martin's review of it) but then also the the directory structure could give some info about the file content. The solution to this would be to tar the whole directory tree and just encrypt this with a coded file name. The disadvantage is that next time you will have to backup the whole compressed directory.
I think that the most convenient way is to copy an encrypted file container on the backup drive and then 1) start a VPN tunnel to the drive for safe transfer of plain text files, 2) mount the drive locally, 3) mount the container locally, 4) copy the files to/from the container 5) detach drive and container. Of course this solution requires the relevant services from the provider (VPN, relevant communication protocol).