I want to make an adventure where intrigue is a major factor.
I am not entirely sure on how to do it.
I'm afraid, I'll have to flesh out a lot of major characters, their agendas and motives, foes & friends etc. Seems like a lot of work.
Much of what I learned about intrigue adventures came from running way too much "Vampire: the Masquerade". In particular, I found the original "Chicago by Night" supplement incredibly useful. I also recommend reading the Alexandrian's blog, particularly the posts about node-based adventure design and the three-clue rule.
Anyway...
I would suggest starting by pencilling in the big factions in your setting. For each of them, indicate what they want, their relative strength, and any special resources they have available. Don't bother with lots of detail at this stage - we're talking big picture stuff. So, if the Emerald Claw have access to a few mercenaries, don't bother to list it; if they have a dragon at their beck and call, though, you want to note that down.
Draw a network connecting the factions that know about one another. (Usually, this means connecting every faction to every other faction, but if there's a secret force out there they can be omitted.) On the connections, note down how these two factions relate to one another. Stick with simple relationships here - The Emerald Claw hate the Silver Flame, and vice versa. Lady Catherine is contemptuous of Lord Borric, but Lord Borric is secretly in love with Lady Catherine. And so forth.
Anyway, that's your big picture stuff. Going forward with the campaign, this will give you a feel for how the various factions will react to the events that happen. Basically, the PCs are going to start plucking the strings... and now you know what music will result.
You're then ready to start getting down to adventures.
The plot in my campaign so far (just starting up), is that there seems to be a framed person that the characters jsut met. He has told the characters his life-story and the characters trust him somewhat.
I want the plot to involve major city officials, conspiracy and even some backstabbing.
Okay, what you have here is an NPC who is associated with one of the factions, who has been framed by another faction. Your network diagram should help you here - pick one faction for the NPC to belong to, pick a competing faction to do the framing, and you've got your villains. (Let's assume our NPC was a member of the Silver Flame; he's been framed by the Emerald Claw to discredit that church.)
Now, build your specific villains as members of your 'enemy' faction. These are specific characters, so try to tie them to the faction in some specific way - if the Emerald Claw has a tame dragon available, perhaps one is a half-dragon child?
From there, work out specifically
how they've framed your NPC, and what trails of clues can lead the PCs back to them.
Be sure to throw in a few characters who are associated with other factions (either as alternate suspects, as complications, as allies, or whatever). And perhaps one or two others who are unaligned - one of my favourites is basically a clone of Inspector Javert from "Les Miserables", who doesn't really care about intrigues, but has an iron devotion to the law, and an unreasonable reverence for titles.
Oh, and one more thing - try to avoid characters who are obviously utterly good and trustworthy, and characters who are obviously utterly evil and corrupt. That makes for a very simple game where the Paladin just uses
detect evil and the party hack their way through the black hats. In my experience, you'll get a more satisfying
intrigue campaign if even the best characters have something of a dark side, and even the worst of villains have some redeeming features. Oh, and
everybody has something to hide, even if it's just that they're embarrassed to admit they enjoy watching reality TV.
How do I turn the characters onto the trail of corruption? Should I leave clear signs or just subtle clues? I don't want to railroad them too much.
In general, for every secret you want your PCs to discover, you want to plant three clues in locations where they're likely to look. Chances are they'll miss one, overlook the importance of the second, but finally 'get it' with the third.
Making your clues obvious enough without being blatant is a bit of an art. My advice is to err on the side of it being too obvious, at least at the start - bear in mind that what is obvious to you with perfect knowledge may well not be obvious, especially when the players only have parts of the puzzle. Bear in mind also that you can always make the clues more subtle as you go along, whereas if they're too subtle from the outset your players are likely to become frustrated.
Can I involve some degrees of success, according to their solving of the intrigue?
Yes. Perhaps the best way to do this is to have some lesser mysteries leading up to a big mystery. As the PCs solve the lesser mysteries, they face a small "end of mystery" encounter. When they solve the big mystery, they face the BBEG... plus anyone else they haven't faced yet.
That way, if they do well they can take down the enemy network piecemeal. If they do poorly, they have a much harder end battle. Either way they get the same XP and treasure, but the 'successful' route is easier.