When does one report to the IRS that one gifted the apartment?
When you've finalized the transaction.
Which form to to use, form 709?
Yes. Make sure to appraise it at the date of the transaction, and read carefully the instructions to the form.
Does the child need to report anything?
Not in the US. You'll need to check the reporting/tax requirements for both of you in the country where the property is located. It may be treated as deemed sale (i.e.: you'll pay capital gains tax), or a gift (i.e.: you'll pay gift tax), or anything else. There may be transfer taxes and fees, and other associated costs.
If I remember correctly, you're in Israel. Having more than one apartment affects how real estate is taxed in your country, so your child may want to inquire.
If so, what form should the child who is receiving the apartment use? and when do they need to do this by?
If the child is a US person, the apartment will probably show up on their Schedule E (unless they decide to live in it, and then it will become their address on form 1040).
Obviously, given the history of your questions on this site, I strongly advise you to talk to a lawyer about whatever it is that you're planning to do.