I cannot seem to talk to other people, but I can hear sounds.

Correction. I can still hear game sounds on my new headset. I just can't hear other people talk.

Hi Pohkii! My name is Ricardo an independent advisor ready to help you with this situation!

In order for you to be able to chat in multiplayer, you must change the privacy settings of your account. It can be done here

https://account.xbox.com/settings

Child's account cant view their privacy settings an adult is required to add him to a Microsoft family here

https://account.microsoft.com/family/

After the adult account creates the family and adds the minor's account to his family

Have you run the steps in Update xbox wireless controller? All controllers you use need to run the firmware update.

The uSB method is my preference.

Before you check for networking issues, can you try the following:

Open up the messages tab on your console and compose a new message (since you don't send it, it doesn't matter to whom you send that message).

Instead of writing the message, press the microphone symbol and record a voice message.

Talk a few words, or goof off. Then finish the recording and listen to your message.

Did the microphone pick up your voice properly?

If yes, do the network checks that OK Fowl linked above.

If not, then it might be that your headset is not compatible with the Xbox controller. If you use a headset with 3.5mm plug and 3 rings on the plug, you should know that there are two standards for these plugs called OMTP and CTIA. Both standards have the
microphone and ground connectors switched.

So if you have a headset that works on iPhones, chances are, that it will not work on Xbox controllers. For that you would need to get a OMTP to CTIA cable (since these cables only switch two contacts, a CTIA to OMTP cable is exactly the same).

And because these cables only switch two wires, these adapter cables are dirt cheap. If you pay more than the equivalent of a coffee to go for such a cable you're being ripped off.

Here is a guide that may help with that issue:

http://xbx.lv/1d3minN