How do I sign my downloaded tax transcript for school?

You do not sign a transcript.  You can get a free transcript from the IRS:

You can get a free transcript from the IRS:   

https://www.irs.gov/individuals/get-transcript

If you are really asking about signing a copy of your tax return--you take out a pen and sign it on the line that says "Sign here."  When you e-file, there is no physical signature on the tax return since it was all done electronically.  If you have someone asking for a "signed" copy--you sign it in ink yourself.

https://ttlc.intuit.com/community/prior-year-return/help/how-do-i-get-a-copy-of-a-return-i-filed-this-year-in-turbotax-online/00/25932

To get a copy of your previously filed returns prepared with online TurboTax https://ttlc.intuit.com/questions/1900748-how-do-i-get-a-copy-of-a-return-i-filed-in-turbotax-online

If your school is asking for a signed copy of your tax return, you'll have to ask them what they will accept as a substitute.  

If you are providing a transcript, instead of an actual tax return (form 1040), I would think a cover letter, with your signature, would satisfy them. 

Sample tax Transcript  https://www.irs.gov/pub/irs-utl/New_Tax_Return_Transcript.pdf