Thanks for using JustAnswer. This is Leela and I will help you with the question today.
By default a Microphone on the laptop is LIVE and it doesn't RECORD and PLAY BACK. But there are programs like a SOUND RECORDER which can RECORD AUDIO, SAVE and you can later PLAY BACK as per your need.
If you have a HEADSET that is good, otherwise your laptop mic should suffice.
If you want to RECORD and then play back that is going to be straight forward and easy.
But if you want to HEAR as you SING (with a delay of few MILLI SECONDS) then it is going to be difficult. But i can suggest you a SIMPLE TRICK by which you can TRY and see how it goes.
If you have a SMART PHONE (Android or Apple or Windows), then you can use SKYPE App on the phone (also have headset for the phone) and also use Skype on the computer. You need to have 2 Skype accounts (which are FREE anyway) and you call from your Skype of laptop to Skype of Smarphone. You will SING onto laptop and have EARPHONES of your smartphone in your ears so that you HEAR via your smartphone that way you can get some DELAY of few milli seconds and you can hears as you sing along. But it is going to be tricky.
if you have headset/MIC for the laptop then it is going to be very easy.
Please let me know if there are any further queries.