I'm hoping I can get some advice re removable media encryption solutions.

I've been doing a bit of reading, and I'm puzzled as to how these solutions work. If I want to find a solution that protects data at rest on flash drives and USB hard drives, what are my options? If the drive is encrypted, and the key is associated with a given computer, how does a user move the removable media from one device to another?

That is, if I encrypt a thumb drive and take the drive somewhere else to do some work, how do these solutions work? Do they have some auto-run app on the drive that prompts me to enter a password to unlock the drive? Does the app get installed when I first plug the removable media into an encrypted drive?

I'm pretty clear on 'encryption 101' - I'm just curious how removable media encryption works when the encryption / decryption application itself might now reside on the host computer into which the removable media might be plugged.

If someone could shine some light on how these solutions work in the real world it would be much appreciated. Thanks.