how to improve your online reputation thorugh search engine optimization?

Definitely social network promotion hits your brand reputation forever. Regular updation in all the medium is not enough, mingle with network audience is vital role in social network promotion. so be in social network always with your users!

That's sure to create great reputation on your quality service.

Another one is , promoting your business in various reputed links. that's also create major impression.

Link building in Quality sites is the one and safe way to improve your online reputation.

Reviews for your website will help you to increase the online reputation.

You can improve your online repution through Social Media as well as through Guest Blogging.

all of these are good ideas. I noted that you are mixing social media and some SEO. All works. Something else would be press releases

By providing what your users want? A quality content can definetly help you in increasing online reputation. Focus on user and their needs to visit any other website.
Google always wants that user satisfaction and if you are doing so, Google will approch you. For that you have to be ready with great, unique, fresh, usefull content.