Quick google search for promoting your business on twitter returned this site as the top result, http://www.chrisbrogan.com/50-ideas-on-using-twitter-for-business/
Make sure you build your buzz and brand by offering value with your tweets. Developing relationships is the key. Don't use the social site as spam.
Both of these sites require that you should build first trust and relationship with your followers/fans/customers, and you should give them value while you're developing your relationship with them. No value no trust and it equals to no profits.
i never do promotion with linkin but twitter is what i am working for and yah, it does give us result but you will need to work really hard to get those ball rolling in
These website are Social networks Sites allow you to find and link to other people. Once linked or connected, you can keep up to date with that person's contact info, interests, posts, etc. Many people are connecting to friends and business associates with whom they had fallen out of touch. It's bringing the world together like nothing else has.
I have used twitter and have gotten some traffic out of it. I have not tried to use LinkedIn yet, but I can say that it is a smart thing to try to use two good resources together. I like to use twitter and google alerts together, and also twitter and RSS feeds.
LinkedIn is not a very popular channel of promotion. Where as twitter can help you in generating good revenue. Here are some tips for business promotion via twitter, - Pick a niche related or Brand related username - Add your website's link in your personal information - Follow like minded people and encourage them to follow you - Publish quality wall posts - Talk about your services in your niche related groups - Distribute coupons and freebies