When filing my taxes, I claim both of my children but somehow I made a mistake and didn't claim one of them so I need to make an amend. Is this an easy process?

The amended forms are not yet available.  The typically become available in mid February.  To do an amendment is similar to filing your taxes.  You will just need to click on the Amend your Return button and then go to the personal info section and add your child that you did not claim. Then walk through the steps to submit your amended return. 

Did you already e-file?  If you already e-filed, you have to wait for the return to be fully processed.   Then you can amend to add the other child.   You will need a special form called a 1040X which will not be available until later in February.

Wait until your original return has been fully processed before you amend, and make sure you have saved a pdf of the original return before you amend.

See this TurboTax support FAQ for amending a tax return - https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-return/amend-change-correct-return-a...

Do not expect quick results from amending. It can take four months or more for the IRS to process an amended return.  

You can watch for information here:

https://www.irs.gov/Filing/Individuals/Amended-Returns-(Form-1040-X)/Wheres-My-Amended-Return-1