I'd start by pointing out that this isn't about 'tournament' scenarios, but if you like 'mini-campaign' scenarios - it's not about figuring out something to amuse X-thousand point armies, but about giving the opposing generals a hopefully reasonably balanced tactical workout that they can, at the same time, enjoy and feel involved in. I'd also point out that far better people than me have designed scenarios for wargamers, and these are just my opinions.
This post will be divided into two parts: first up, preparation. (OK, let's be honest here. On my past form? at least two parts!)
Basically, the first question you need to answer is 'why are the opposing forces here?' The standard tournament answer ("Because they ran into each other, duh!") generally Won't Do - armies don't, normally. One side or other will have an objective, which may or may not be known to the other side, and is usually on terrain of the other's choosing. Some of the more interesting, particularly smaller-scale, battles, focus around taking small strategic objectives like river crossings (Pegasus Bridge) or villages, or covering retreats (Quatre Bras). Sure, that objective sometimes is 'bring the opposing army to battle and crush them', but even then there's a story - look at Waterloo for an example.
Make them fun. Go to a little bit of effort - they can just be verbal briefings, but you could prepare handouts.
Briefings should actually be in two parts: the mission, and, for want of a better word, the knowledge.
If you like, you can consider the mission briefing to be the victory conditions. It could for instance be an in-character communique from the commander's superior officer telling him what his goal is. For extra verisimilitude and immersion, take advantage of modern computers and printers, and use a suitable font as well. I've done at least one mission brief (which those of you going to Hammerhead will see at our club's participation game) with authentic German stamps and Himmler's signature!
The knowledge is the stuff that the commander should know as well as the mission brief - why he's where he is, what condition his forces are in, etc. This can also be used to set up and justify some of the rationale behind the scenario - for example, in one of my Op: Squad scenarios, the German squad (attached to a Flak unit) is transport-less because the Feldwebel of the overall detachment has driven off in the Opel Blitz to visit his (presumably French) girlfriend. It can also be used to set up personal aims for the commander (or commanders, if you're expecting multiple players a side). Above all, it can and probably should be entertaining, something that draws the player in.
On top of that? Maps. Always! Maps are cool: even if they're just sketches. Better yet if you can use one of the cheap or free graphics packages to pretty them up a bit. (For the Mac, OmniGraffle's really neat and not that pricey. For the PC, it's a complete no-brainer - just buy Campaign Cartographer and the Dungeon Designer add-on! (note for Mac users, this will run under CrossOver.)
If you want to see some really masterful attempts to impart knowledge, go grab a copy of Don Featherstone's Skirmish Wargaming, and read some of the two and three page pieces that precede each scenario - they are, to all intents and purposes, short stories. While there's probably considerably more information in those than is absolutely necessary, they do make for excellent plots for scenarios.
This is always a tricky one. The briefing is the primary place where you can tune game balance: number of units available, timings of arrivals, etc. For example, a lot of my Operation: Squad scenarios are designed for equal forces, but compensate for one side being in good defensive positions by requiring half of them to roll to wake up. If you're running with an umpire, it also allows you to add unknown numbers of reinforcements to either side at a later stage in the battle, if things are getting a little one-sided.
Of which, more next time. Enjoy!