That's a good (and complicated) question, Molly! First of all, let me preface this answer by saying that I am not a tax attorney, CPA, or other type of tax professional. So, I still suggest seeking advice for your particular situation.
That said, you can certainly claim depreciation for the time between when you buy your second home and the time when you move into it, provided that the property is made available to rent to tenants. In other words, if your cost basis in the building is $200,000 (remember, you can't depreciate land), based on the 27.5-year depreciation schedule, you can claim a depreciation deduction of $7,273 for the year you use it as a rental property.
Depending on the timing of your move, there are a few other things to keep in mind. For example, if you bought the property midyear, you'll have to take a prorated depreciation deduction for that tax year.
A similar concept applies if you sell or move into the property in the middle of a calendar year or if you use the property for personal use as well as for rental purposes in a particular year. For example, if the home is rented for 40 days this year and you personally use it for 60 days, you can only take 40% of a normal depreciation deduction.
Obviously, you should stop claiming depreciation deductions once you move into the property on a full-time basis. However, it's also important to keep in mind that the depreciation deductions you claim will follow you until the property is sold. This is called depreciation recapture, and the general idea is that any cumulative depreciation deductions you've taken will be treated as taxable income once you eventually sell the property. If you aren't planning to sell for the foreseeable future, this probably isn't a big deal to you, but it's still important to know.
Furthermore, it's worth mentioning that you'll need to deduct things like mortgage interest a bit differently while you're still treating the home as an investment property. The mortgage interest deduction only applies to taxes paid on a qualified personal residence, not investment properties, but you can deduct your mortgage interest as a business expense to help offset your rental income. The same concept applies to deducting property taxes.
As a final thought, I don't know how you financed the property, but if you used a second home mortgage (as opposed to an investment property loan), it's a good idea to check with your lender and make sure you're allowed to rent the property out to tenants.