follow them! that's what online marketers do. when you're new, they follow you and they expect a follow back... do the same.. i can see a lot of twitter users gaining thousand of likes maybe in a week because of it.. and also dont forget to post meaningful tweets that your followers will relate to. at least every minute so theyll see how active you are.

One trick that I like to do is find another Twitter profile that is similiar to your niche and market and than follow the people that comment on their statuses and even their followers crowd.

60 Simple Ways to Increase Your Twitter Followers - Advanced Lead Generation Marketing Blog
You can read this to gain twitter followers.

The Best way to gain twitter followers is follow other twitter users who are dealing with same business, similar websites, services etc. If you follow them then they also will follow you. It is the basic and best way to increase followers.

I have some entirely free (valuable and interesting) information (actually posted on a related forum) that I would like to share with as many Tweeps as possible

I managed to get two RTs from guys with quite large follower numbers (25k+ each)

have you any suggestions for how I can get many more people to see the link?

I'm going to have to disagree. Most of the people you do the follow-for-follow thing for will just unfollow you as soon as you follow them. What's the point? Plus, they're not interested in your twitter feed whatsoever.

First of all, tweet interesting stuff. Buy custom one-liner jokes on Fiverr. I'm talking stand-up style one-liner jokes, and new stuff, not stolen jokes.

Next, just get involved on twitter. Follow people you find interesting and then respond to their tweets. Even celebrities. I've been retweeted by MAJOR celebrities MANY times just because I responded with something funny to their tweet. And guess what? That led to a ton of REAL followers who actually somewhat care about what I'm tweeting.

You can browse through people's tweets to see which ones retweet a lot. If they do, and you like them, follow them and respond often. And retweet them often, too!

hashtags favorites and retweets all peak people's interest on twitter

Search for users in your niche and follow them.

It's the easiest and fastest way to get followers. Sure some may not follow you back and some may unfollow you, but if you tweet useful and relevant information you can grow a loyal (and maybe even profitable) following.

For smaller niches, target them specifically and interact with them. Like for example "favorite" or follow users whos tweets contain #warriorforum to target warriors (very basic example).

You can use numerous services to completely automate this process and target hundreds a day.

When you 'favorite' or follow or retweet someone, they generally get an email notification and notification on twitter that your profile interacted with them, and if that profile is your business name/website logo/etc; and it's relevant to them because you should have targeted them well, then they get intrigued and that means more eyeballs to your website/product/service, automatically.

Yes.. best way is to follow them.

I've done the follow-for-follow stuff, and while it builds up your numbers fast, it won't really be of much value, EXCEPT that people are more likely to follow you if you already have other followers. Right? No one wants to be the FIRST one to follow someone. That feels uncool. But if you already have 2000 followers, that newbie that just might turn into your biggest customer ever won't hesitate to follow you as well.

Oh, and GOOD CONTENT. Don't just tweet to do it. Make it worth someone's time to read.

search for tweeters who are in the category that you like, follow them and follow their followers. You should get those who have high followers

I would say also stay consistent with your tweets, retweet others, use hashtags, and have fun. Share inspirational messages, value, and "invite" people to things. Don't just blast your site all over the place. The more you personalize your account, the more people will be attracted to you.

to share funny and unique things on twitter may be the best way to attract follower.

install IFTTT and let all your new blog post be published on twitter and other social networks.

Just like any other medium, Twitter audience is also directly proportional to the value you are providing to the people. Figure out your target market and help them with their problems selflessly.

You will be surprised to see how much appreciation you get, whether it's in the form of followers or business leads from people.

Follow for 3 days and if they don't follow back... cut em

Good Luck