Recording a podcast remotely may pose some challenges when recording with a guest or co-host.

You have two options for recording the audio of your podcast, you can...

record the conversation through an online software (Anchor, Zencaster, Zoom) in real time, or
record separate audio for each guest or co-host, then edit the audio together following the conversation.

Regardless of how you record the podcast, an external microphone will enhance the quality of your audio. If recording through an online software, a USB mic (I use a Blue Yeti, but the Audio Technica ATR2100 is another versatile option) or an external mic plugged in to your computer’s headphone jack will sound better than any built-in microphone.

If you plan to record the conversation in real time, you’ll need an online software that allows you to host your conversation while simultaneously recording the audio. Here are some popular software options with a brief description of features:

Anchor (unlimited storage, free hosting, limited editing software)
Zencaster (8 hrs. of recorded audio for free per month, up to 2 guests, export as single audio file)
Zoom (record a single conversation up to 40 mins. with 2 or more guests, creates an audio and video)

Things to remember:

Audio quality will suffer when recorded through an internet software.
If your guest or co-host does not have an external microphone, encourage them to wear headphones during the conversation to avoid feedback.
You’ll get better audio quality recording the files directly to each of your personal computers, then editing together the podcast following the conversation.
Auphonic allows you to upload your audio a lot of the leveling and noise reduction automatically (2 hours per month free)

Good luck.