I've had quite a bit of success running Twitter ad campaigns for @socialharvest actually. The product (free software) isn't done yet, but jumping on social media early is important.

You should build a presence as early as possible for any product. You can't just be done, go live, and say, "Hey world! Here you go!" ... You'll then say, "Wait, world? Where are you?"

You don't need to spend a lot of money to be frank. You'll want to run a campaign targeted at getting newsletter sign ups or something. This is probably one of your goals anyway before product launch (and still should be after!).

Those types of campaigns (lead generation campaigns) cost a lot less on Twitter when you target them very narrowly. You also get a much higher engagement rate AND they bring you new followers too (without cost). Whereas a followers campaign on Twitter is far too broad and will burn through your ad budget FAST...For followers who are unqualified (could even be spammers) or who unfollow you anyway.

Then you'll want to do the same old grooming techniques blogged about a million times out there. Follow a few people and unfollow those who don't follow you back. Though I'd add to that, follow relevant people and it's ok if you don't unfollow some just because they don't follow you back. If they are relevant...Well? Why not?

This brings me to the last point:
Use social media! That's how you build a presence.

There's no quick trick really. It takes constant time and attention. However, I think you can truly spend a few minutes a day sharing relevant/related links/content, following people, retweeting/favoriting, and be just fine. You should see your followers build nice and steady. Without coming off like spam.

This strategy is great for Twitter. For other social networks it's similar, but different and there may be one network that works better for your product too.