There are plenty ways to make money online and Twitter is one of them.

Crowdsourcing
This involves soliciting ideas and contributions from a large group or community. If done correctly it can make you plenty of money, or at least capital for your business or idea. The best way this is done is tweeting to your followers to bring in contributions to fund your business or idea and asking them to help 'retweet' to spread the word. Some marketing expertise needs to learnt to successfully market your business or idea in order to get positive responses.

Produce a Twitter Related Service
You already know that the majority generally use Twitter during their free time, you can take advantage of this by creating a product or service that will appeal to them. A similar product or service might already exist but you can create a better or cheaper one that the users will know and love you for. For example, you can charge people to help them build a Twitter presence and make your prices reasonably and attractively low.

Sponsored Tweets
Companies and businesses are willing to pay for your tweets, just as long as you have a large enough following. You can find sponsors willing to pay you to Tweet about their products for an arranged fee.

Twitter Contest
A contest is one of the most effective ways to engage people on Twitter. You can try linking up with a local business that wants publicity, offer to hold a contest on Twitter to help them with this publicity and ask to be paid a percentage of sales that come in. Be sure that everything is as legally binding as possible to avoid being cheated. There a lot of fun and enticing ways to engage followers in a twitter contest, just brainstorm a little on it.

Sell Your Own Products and Services on Twitter
This might seem obvious but the funny thing is that a lot of people don't recognize it. Many people aren't using Twitter to effectively sell their products and services; this unfortunate because Twitter is one of the best ways to do so. Be on the lookout for and take advantage of trending hashtags related to your products and services and use this opportunity to put your work out there for not just your followers to see. Remember, 'a little self-promotion can quickly lead to a job.'