[RPG] How to easily come up with improvised dialogue

A technique I use is to try to emulate audio description narrative, the techniques developed to help people with vision impairments enjoy movies. A really good (free) example can be found for the Wind in the Willows (dead link).

The WGBH link to Wind in the Willows has been archived by the station. Similarly free and available is this potentially-different reading of Wind in the Willows available here.

Assuming everyone's interested in doing this, it will be difficult to break existing 15 year habits, so you have some work cut out for you.

1. Get everyone's buy-in. Explicitly say that you want to go heavier RP and make sure you all have a common understanding of what that means. That's not a panacea - I did the same thing, a group agreed they wanted to go more RP heavy, but after we started a couple people clearly didn't want to (or, more likely, misunderstood what that meant to me). We had a large enough group we just split it - serious RPers played Sundays and casual kick-in-the-door types played Wednesdays.
2. Consider whether you want to create tangible rewards for RP. "XP for roleplay" sounds good but often falls down in various ways - creates concerns over favortism, ends up promoting the wrong behaviors, etc. I've worked with variant mechanics like "players vote for best RPer of the session and they get XP" or handing out temporary bonuses/bennies that don't permanently augment your character for roleplay. Nowadays, I never give XP for RP (not only because I've given up on XP as a lame antiquated notion) and only sometimes/seldom give bennies, I think that maybe has its place but has a lot of downside - and isn't really necessary (see point 5 below).
3. Get practice. Here's the deal - if you have a 15 year group that doesn't RP but wants to, they don't know how. There's no shame in that. Like when you start anything else new, some training and/or practice can be good to get you on track. Try some one shots of very rules light pure-RP games, things where there's practically no combat and everything's "downtime." Then people will take techniques they learned from that back into their usual game.
4. Don't punish RP. One of the classic errors I see people make is say "I want roleplaying" but then using any non-by-the-book things characters bring up during RP as ways to get at the characters - in their mind "interesting developments," but in the players' minds "I better keep my mouth shut around NPCs because it always comes back to haunt me." Or when they choose suboptimal tactical options/gear/etc. for roleplay reasons, try to respect that and not punish them for not just min-maxing without regard to RP.
5. Reward RP. Not with XP or tangible rewards, but with increased understanding of the game world and relationships with its NPCs that benefit them. Taking the time to understand who's who in a city and to forge relationships with them gets you favors, they tell you rumors, they cut you discounts... You know, all the benefits you get in real life from not being a sociopath. (The average "tactical" PC is a clinical sociopath from the point of view of the game world's inhabitants.) If a player can get just as good results through unremitting murder - why wouldn't they?
6. Give them RP opportunities. This is challenging to you as a GM - it's where the burden of a RP heavy game lies, but if you step up then the players will respond. @wraith808's answer is a good example - you always have to be opening the door, having people around, reaching out to the PCs, opportunities to do something interesting-but-not-tactical. Players just trying to figure out RP may be passive and you may need to push the opportunities on them more aggressively - instead of "oh maybe that chick needs help with her wagon" it could be "man this lady is sweating me for orphanage donations like every single day, and won't stop talking about it!"