My practice is primarily taxation - I am an Enrolled Agent, doing representation (including tax litigation), research and complex tax situations. Most of my clients are other tax practitioners or attorneys on behalf of their clients..
On the new forms, income can be placed on Schedule 1, but the line numbers are mostly the same. Notary income is recorded on Schedule C, which bubbles up to Schedule 1, Line 12.
The Schedule C is relatively straightforward, and can bear the same name as the taxpayer. Expenses are defined in categories; the form, as a whole, can clearly present the taxpayer a picture of how profitable their notary services.
Only the statutory notary fees per notary act are exempt; for example, in NY it would be $2.00 per notarial act (i.e.: acknowledgement or jurat). This comes from regulations covering fee basis public officials, specifically Treasury Regs. 1.1402(c)-2(b)(2).
If the taxpayer had no other income subject to SE tax, enter "Exempt—Notary" on Schedule 4 (Form 1040), line 57; the taxpayer should not file Schedule SE. However, if the taxpayer had other earnings of $400 or more subject to SE tax, enter "Exempt—Notary" and the amount of their net profit as a notary public from Schedule C or Schedule C-EZ on the dotted line to the left of Schedule SE, line 3. The taxpayer should then subtract that amount from the total of lines 1a, 1b, and 2, and enter the result on line 3.
FYI, the 2017 1040 more resembles its 1917 predecessor, than its current year (2018) version!