HDD "adapters" are everywhere! I believe you can even get one at, or at least through Walmart even. The only question is what do you have now and what do you want to plug it into.
You said you have a desktop SATA drive which means it's likely a 3.5-inch HDD. You need to know this for any physical fit to the case. (Laptop HDD's are almost always going to be 2.5-inch varieties.)
Then you definitely said your desktop HDD was SATA. Again, that's very common so it would be hard to get an incompatible "external HDD enclosure." But be aware that there are still a lot of PATA adapters/enclosures so those would be ones to avoid.
And once you get your desktop HDD in your new enclosure (the one with all the data), it's really just a matter of plugging it all in and turning it on. You probably would need to worry about drivers or format types if we were talking about anything other than Windows. But it's probably safe to assume that your HDD was formatted/prepared using an NTFS or FAT type file system. Therefore almost anything can read it without any other special considerations.
Of course, there may be issues with file permissions and ownerships with whatever else wants to access those files, but it too is almost never an issue. Just plug and play - literally!