If my site gets clicks from LinkedIn both from ads on LinkedIn and from posts or things other than ads (on LinkedIn), how can I track clicks from the LinkedIn ads in Google Analytics?
You should tag the URL of your ads: see http://support.google.com/googleanalytics/bin/answer.py?hl=en&answer=55578 for more information
Well, traffics from both LinkedIn ad or posts/links will show up in Google analytics under the traffic source LinkedIn.com. That should be enough. Or do you want to separate the visits from ad click and simple link click?
This tool from Google will let you create URLs for your LinkedIn ad campaigns with specific tracking parameters. https://ga-dev-tools.appspot.com/campaign-url-builder/