I find that the concept of New Year's Resolutions isn't really widely known in Japan, so I start out by explaining that in the US, we try to make goals when a new year comes. In Japan there's a bit of a similar feeling when the new school year and fiscal year starts in April. To show an example, I write up a couple of my goals on the blackboard, depending on what grammar points the students are familiar with:
I write a couple of mine, make sure the students can understand them, and then ask the JTE if they have any. Hopefully between the two teachers, the students will have a good battery of examples to draw from. You might want to write up some more verbs or ideas to help the students think of relevant language for their goals.
Next I pass out the papers and ask the students to come up with two their own resolutions. After they're done writing, I ask them to ask each other about their resolutions. Remember to remind them to change the pronouns ("He will practice baseball every day.")
If you're confident that they won't lose the papers, you could check up with them several months later (or even at the end of the year) and ask them if they've kept their resolutions!