Advertising opportunities are obtainable through Google AdWords. These opportunities enable you to bid for non-exclusive presence in various locations on the LII site. Learn more about Google AdWords.
So which will work best for you? Sponsorship is a better deal because with direct sponsorship ads you aren't paying a middleman, you get exclusive sponsorship of the entire page, and you don't compete with others for impressions. But if your LII advertising budget is under $1000 a month, Google AdWords might be the place to start.
Here is our Google Ad Planner page with more information.