As long as you understand the general concepts of the game, and have at least some experience in playing it, I'd say that's enough. You're probably not going to create the next "No added colors or Lemmings"* when you've just started designing levels, regardless of how much playing experience you have - but that doesn't mean you can't create decent levels; plus the best way to learn something is to practice it.
* "No added colors or Lemmings" is Mayhem 20 of the original game, and according to voteoffs and past discussions here, the most popular level in Orig.
In terms of what I do with ideas - generally, there's only two processes that tend to happen:
A) Level appears in my head. Level is transferred roughly to the editor, then touched up until it works.
B) Editor appears on my screen. Pieces are randomly thrown together until something resembling a level appears. From this, the level is touched up until it becomes something good.
(Of course, some levels are a combination of both of these. Often the main trick will come from method A, while the rest of the level - the context in which the main trick is hidden, especially if it's some kind of crowd control trick - is devised using method B.)
As counterlogical as it may seem, in my experience the better levels I've made tend to come from Method B, including my (so far) most popular level, "Panic Attack" (Genius 8) from Lemmings Plus II. This doesn't mean that method A should be discredited altogether, of course - some great levels have come from that too, such as "An Unexpected Journey" (Genius 18) also from LPII.
A third, but rarer method, that I sometimes use (and could be considered a variant of Method B) is that I'll come up with a general concept for a level, but this will be quite an abstract concept and the actualization of the idea is pretty much "slap together something that works" still. A great example of this is "To the end!" (Psycho 28) from Lemmings Plus I; I had the concept (see below) beforehand, but the actual level it existed in was made up as I went.
(I've hidden the concept here behind spoiler tags, since you mentioned elsewhere that you planned to play LPI at some point soon, and so you might not want to be spoiled on this.)
The concept here was to take the common (particularly in the Master System version) idea of "a level with 20 of most skills, but one or two that there's none of", and make that "none" skill builders, in a very complex worker lemming-like level where builders are very valuable (but it is possible without them).
New ideas show up more often than you think. Especially if you use NeoLemmix or Lix, as they have new skills and other new features that haven't been explored too far yet. Even if one of your ideas isn't new, you're most likely combining it with other ideas in a different arrangement than previous levels have, or hiding it or setting it up in a different way, etc.
Some things I would recommend avoiding though, as they're kinda annoying and have been done to death (and I myself have done some of these in the past xD) - excessive use of hidden traps; invisible/hidden exits; and the "I am A.T." trick*. Of course, if you can come up with an original way to use those, then by all means do so - that's a different matter if they're used in a original way.
"I am A.T." is a level from the Genesis version of Lemmings; the main trick of it has been done to death in custom levels. It involves...
...placing a line of diggers one next to each other, so that they end up creating a somewhat diagonal slope and/or over their combined width destroy a whole wall.
The flip side is that existing levels can be a great source of inspiration. Don't copy them exactly, but think about how you can get new ideas from them. Perhaps when you were solving a level, you spent a long time on a really neat idea that almost works -- in your own level, that could be the real solution, and the solution to the source level becomes the red herring. Perhaps you find an interesting solution to a 20-of-everything level -- then you can reduce the skills enough to enforce it, or add obstacles that block off certain routes.
This is how I made "You Only Get One Bash At It" -- I can't discuss it without a certain amount of spoilerage, so I'll hide the rest (but it's not a complete spoiler of the solution).
I started from the solution of mobius' "Exit stage right" and flipped it around so that the solution to mobius' level was the plausible red herring in my level.
The level that resulted turned out to be the hardest, and perhaps also the best, level I've ever made. The fact that it was closely derived from an existing level doesn't hurt it at all.