The old click to agree, If people submit entries online, for example, at your website or at a third-party site, you can have a button tied to a statement that says something to the effect of: "By submitting your entry you agree to give ________ the right to republish this material in all formats and editions of ____ Dictionary." You can be more detailed and explain additional uses you wish to make for the material. Generally, any assent you can get as a condition of the submission will be fine. If it seems a little tricky to set that up at your website, it's pretty easy to set it up at a site like SurveyMonkey.com. Just direct your entrants to a survey you create there and include the statement by the final "Submit" button. (It probably shouldn't be an issue for a dictionary, but some companies also ask the entrants to agree to the fact that submission is original to them.)
Contest Rules. The Dear Rich Staff also suggests that you can shore up your position by listing your "contest rules" at your website -- for example, by including a similar permission statement in your rules webpage. You will also need permission if you are posting the name, photo or any other personal information about the contest winners. And finally, if there is some kind of remuneration for winners - whether gifts or money - you should take a look at national contest laws (for example, any contest worth more than $500 is probably invalid in Rhode Island). Wow, this is starting to get as boring as a bunch of contest rules. We'll stop now.