First: who made the mistake?
There are two kinds of I-94 records, and a different office fixes each one.
CBP made it: the record from your arrival at the airport or border. CBP fixes it at a Deferred Inspection office or at a port of entry.
USCIS made it: an I-94 attached to the bottom of a USCIS approval notice (Form I-797A), for example after an extension. USCIS fixes it with Form I-102.
Do not file Form I-102 for a CBP mistake. USCIS will not fix it.
Download your I-94 again from i94.cbp.dhs.gov to be sure the error is real.
Search "CBP Deferred Inspection Sites". The page lists more than 70 offices, mostly at airports, with phone numbers, emails and hours.
Choose the office nearest you, or the airport where you arrived. Many offices accept requests by email and do not take walk-ins. Read the office's own instructions.
Send or bring: your passport, the visa page, the I-94 printout, and the document that shows the correct information. That is the I-20 for F-1, the DS-2019 for J-1, the I-797 approval notice for H, L or O, and your marriage certificate for a dependent spouse.
Write one short paragraph: what is wrong, what it should say, and when and where you entered.
When it is fixed, download the I-94 again and save the new copy.
If the error is on an I-94 that came with a USCIS approval because of a USCIS error, file Form I-102 and say it was USCIS error. There is no fee in that case. For other I-102 requests the fee is high ($560 plus a $24 I-94 fee in the current fee schedule), so make sure the mistake was really made by USCIS.
Errors worth fixing quickly
Name or date of birth wrong.
Wrong class, for example H1B instead of H4, or L2 instead of L2S. The S code is what lets an L-2 or E spouse work without a separate card.
An end date that is too early, for example a worker given 6 months instead of the approved period.
A student who got a date instead of D/S.
Waiting until the old date is close. An unfixed early date counts. Act in the first week.
Asking your school or employer to fix it. They can help with letters, but only CBP or USCIS can change the record.