I got my Stem extension last year. Here are the following things I would suggest.

1. Make sure to send your application before your current one expires. They should receive your extention application before the expiration date on your current OPT. 
2. Same process as your first OPT. All documents same. Except this time you will have one more I-20 for STEM extension. This new I-20 contains the E-verify number of your employer.
3. Letter from your current employeer. This is optional, but helps to make your case strong. I didn't submitted the letter from employer.
4. Make sure to contact your International office for the process of getting new I-20 with E-verify number. Requirements might differ based on your school's policy. My case, my HR send an email to my International Office providing them with e-verify # . And the college issued me a new I-20.
5. Last but not least, don't be lazy. There were many threads ( in Sajha) in past asking same question. There is some thing called Google.com     Go there and on textbox type, "STEM OPT Extention process and document"

Happy Weekend !!