So, long story short, we killed a warlock and looted him. We found his spellbook from Pact of the Tome. Now, because I am also a warlock (at least I'm assuming that's the reason since he wouldn't let the cleric or wizard do this), I could sit with the book and try to learn the spells. I learned 2 cantrips.

My question is: how do I add those spells to my list on D&D Beyond when I don't have a specific feat or item or whatnot that lets me add them? I've tried looking into adding something to my equipment like a scroll or spellbook, but those don't let me add spells to my actual spell list.

Anything helpful would be appreciated.

You can add them with a custom magic item or a custom feat.

Any chance you can do a walk through on how to do that? I'm not finding anything I can work with. But thanks for the info nonetheless!

Create a homebrew feat that adds 2 spells, then add it to character by clicking manage feats.

The Pact of the Tome book of shadows does not provide levelled spells. It's 3 cantrips which cannot be learned. And the books turns to Ash when the warlock dies.

You're well into homebrew territory here so there's nothing official we can help with.

There are two ways you can add the spells:

Magic Item or Feat - you can make a feat or magic item to add them. This is easier but will not let you cast via spell slots. It will either show At-Will or set charges and manually mark off your spell slots on use.

Homebrew Subclass - you can copy the subclass you're using if it is one you have purchased or is free. You can then add a feature to add these spells and they will be usable with spell slots. 

If you look at the actions section there some small red text. It says manage custom. You can add actions and spells. I don't know when this was added but if anyone finds this chain from now on now you know.

Quote from BuhBuhBradski >>

If you look at the actions section there some small red text. It says manage custom. You can add actions and spells. I don't know when this was added but if anyone finds this chain from now on now you know.

 
This adds an action that has a similar structure to spells but is not the same as adding a spell - it will not be listed in your spells section and cannot be "cast" to automatically mark off a spell slot.