If you paid someone for $600 or more in services (not products) in the course of business (this includes rental properties), you are required to provide them with Form 1099-MISC.
In your case, you will need to provide the leasing company with a 1099-MISC (unless they operate as a corporation) and you will not need to provide one for the garage door repair.
If you need to prepare and file 1099s, they are available on the IRS website (https://www.irs.gov/pub/irs-pdf/f1099msc_16.pdf will take you right to the form).
Please note that, in order to file your 1099s with the IRS, you are also required to provide Form 1096 (https://www.irs.gov/pub/irs-pdf/f1096_16.pdf), which summarizes the 1099 information.
Filing instructions, including the IRS mailing address, are included on the face of Form 1096.