I am going to assume you are not clergy. As a part time worker, you should receive a 1099-MISC from the church which you will report on a schedule C. The form SE will then be used to calculate Medicare and Social Security taxes as part of your tax return.
Please click on the following link for more information Report income without taxes withheld.
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You need to report all your income even if you don't get a 1099Misc. You use your own records. You are considered self employed and have to fill out a schedule C for business income. You use your own name and ssn or business name and EIN if you have one. You should say you use the Cash Accounting Method and all income is At Risk.
After it asks if you received any 1099Misc it will ask if you had any income not reported on a 1099Misc. You should be keeping your own records. Just go through the interview and answer the questions. Then you will enter your expenses.
Self Employment tax (Scheduled SE) is automatically generated if a person has $400 or more of net profit from self-employment. You pay 15.3% SE tax on 92.35% of your Net Profit greater than $400. The 15.3% self employed SE Tax is to pay both the employer part and employee part of Social Security and Medicare. So you get social security credit for it when you retire. You do get to take off the 50% ER portion of the SE tax as an adjustment on line 27 of the 1040. The SE tax is already included in your tax due or reduced your refund. It is on the 1040 line 57. The SE tax is in addition to your regular income tax on the net profit.
Here is some IRS reading material……
IRS information on Self Employment
Pulication 334, Tax Guide for Small Business
Publication 535 Business Expenses
You can enter Self Employment Income into Online Deluxe or Premier but if you have any expenses you will have to upgrade to the Self Employed version. How to enter self employment income