GreyMasker: That makes sense, thanks for the advice! I guess I wasn't thinking that the progress of the games was as linear as all that, good to know.
You can very easily play both games "at the same time", by which I mean, you can do some things in Clouds of Xeen and then head over to Darkside and do a few things, and keep switching whenever you want. But as others have said, the games were originally released separately and so it's completely possible to just do Clouds in its entirety first, and then tackle Darkside. Darkside was designed to be harder, but still possible to start with.
Because the GOG version has the two games merged, it's not possible to just start a new game in Darkside. But as sethsez pointed out, you can very easily walk there from the first town in Clouds. If you want to use a trick, you can take some characters to Darkside, sign in at the inn, and then make new characters there. Characters made in Darkside start at level 5 instead of level 1, because of the increased difficulty in Darkside. However, this is totally not necessary, as your level 1 characters will have plenty to do in Clouds.
I'd recommend just starting in Clouds and then switching over to Darkside whenever you feel like to try some quests over there too. You'll probably find that you'll spend most of the early game doing Clouds content since it's easier than the Darkside content, but you can definitely tackle the first 1/4 to 1/3 of Darkside while you're finishing up Clouds. Then the high-level endgame stuff will primarily be in Darkside. One cool thing about the games though is that there is some special content that's specifically designed to take you back and forth between the two games, like certain dungeons in Clouds that can only be unlocked with keys found in Darkside. I thought it was a cool touch.
Anyway, enjoy, they're really great games!