Generally, you gather a group of 3 others whom you trust to be good, and you start at Emberlight. That way by the time you get to the Clockwork Terminal, people have pills, remedies, and vitapods.
SLs can be soloed, but I don't suggest you try to do so.
For the mechanics of how exactly you enter a Shadow Lair, which ones you can choose, etc., read the wiki article "Shadow Lair".
As far as recruiting goes, I recommend that you take along three trusted, respected friends/guildies. You don't want any party member leaving in the middle of the run because he forgot that his mom wanted him to clean his room. Also, they should all be correctly equipped for that particular Shadow Lair. Unless you want to be generous, they should agree to pay their fraction of the Shadow Key cost.
Further, you might consider finding a friend who has done the Shadow Lair already, preferably more than once. As in every part of the Clockworks, practice makes the fights much, much easier. On the other hand, if you're looking for maximum excitement, go in with an inexperienced team. The group sensation of "holy cow, there's another wave!" is wonderful.
On the forums (usually in General Discussion) you can sometimes find threads where people recruit Shadow Lair parties. I've also seen people asking in Haven. That seems dangerous to me --- your random teammate might be incompetent or a jerk --- so ask some probing questions.
Your question is so...
How do you find a party for a non shadow lair level/mission? You either invite friends, guildmates or pray for good random players.
You solo if you think you're good enough.
Shadow lairs are no different from that.
I'm not sure which "half" I'm in, but people might be responding to your thread title, which is misleading. You could edit your thread, changing the title to something like "How to recruit for Shadow Lairs?" (if that is the point of this thread). Then you might get better responses.
I didn't address your "are Shadow Lairs worth it?" question. For that, you might search Google for something like "spiral knights forums shadow lair worth". You'll find threads like these:
http://forums.spiralknights.com/en/node/88413
http://forums.spiralknights.com/en/node/79984
http://forums.spiralknights.com/en/node/39861
Well, if you are willing to spend the entire costs shadow lairs are very to solo in normal and in fact easier than with 4 members, I discovered that while doing the ice queen, one of my party mates had to go to work, the other one had to clean his room and go to sleep, and my friend had a disconnection problem and left, then cause I didn't want to lose the key I tried to it off alone, and I did it with 4-5 deaths in to total, excluding the free revives.
If everyone in your party has the perfect equipment for the SL, then you have nothing to worry about.
You go to CW terminal with your party. ONE shadow key is required to open it for your ENTIRE PARTY. Seriously, it's on the wiki. And SLs can be soloed.