Hopefully you had a pre-launch page where you collected email addresses, then you can email these people upon launch.
Facebook or Google cpc ads.
Submit your site to business/product directories.
Post about your web app on relevant forums (ie. if it is an app to help accountants, find some accountant forums to post on).
Join linkedIn groups and post about your app in there.
Create a facebook page/twitter and post updates regularly. Include these on your webpage, in your email signature and try to get as many likes/followers as you can.
Cold call/Cold email anyone you can find that are potential customers.
If you can find news and other interesting items related to the web app, set up a Twitter, Facebook group, blog, Tumblr, etc. and shovel a couple pieces of content on there a day. Search Twitter and follow everyone talking about that niche, retweet their stuff, do the follow Friday posts, etc. (Take a look at http://challenge.co for more ideas on testing the market first, which you can then use to promote your app.)
Hopefully you had a pre-launch page where you collected email addresses, then you can email these people upon launch.
Typically this is a pre-development page, whereby you're basically tricking people into thinking you already have something, just to gauge the viability of what you're thinking of building.
It doesn't have to be pre-development. For my product, I created this page about 3 months after development began, and 3 months before public release. I used the signups to get beta testers before launch, and then announced to the rest after launch.
Anything can be a sleazy practice if people use it for sleazy purposes, but it's not the practice itself.
I've seen people recommend doing exactly what I described. Obviously, being honest about what's up is not a bad thing, but that's not what I was talking about.
What's wrong with gauging interest? If people are genuinely interested in what you are proposing (whether it is built or not), they are genuinely interested. They will remain genuinely interested when you are eventually done with the product and ready to launch.
If you are solving someone's problem, they will be happy regardless of your development state.
Facebook or Google cpc ads.
Submit your site to business/product directories.
Post about your web app on relevant forums (ie. if it is an app to help accountants, find some accountant forums to post on).
Join linkedIn groups and post about your app in there.
Create a facebook page/twitter and post updates regularly. Include these on your webpage, in your email signature and try to get as many likes/followers as you can.
Cold call/Cold email anyone you can find that are potential customers.