|Content is king|
If you help them solve a problem or fill a need, they will be comfortable coming back to you for help in other things and if you chose that connection because they may be an Ideal Client/Customer that means you get the first shot at solving problems that benefit you both.
The content you share can be links to articles (Curated) with comments, Videos, articles you write, blog posts or anything of value to your connection. Your success depends on the quality and appropriateness of the content you share.
Obviously original content does more to build your authority on a subject, be wary of plagiarism or trying to make an article someone else wrote be your own. It's one thing to take knowledge you gained through reading and write your own article but copy and paste is not advisable, ever. Remember if the topic is relevant, the connection may have already found and read that same article and if so he will see it in your article and you lose all credibility.
Keep it personal and pertinent to your ideal client/customer and you will do fine, even if you miss the target on a share, don't give up, your new connection will appreciate the thought and the effort.