Do you know how to make an Item? That's all you need to do, basically, and just register whatever Icon you want for that item. Override #onItemUse, #onItemRightClick, and, if you want to spawn child entities, #onRightClickEntity, then copy/paste the code from the vanilla monster spawner item methods of the same name, change it to spawn your Entity instead of using the EntityList, and bam, you're done.
I made a custom entity (mob) but I don't know how to add a custom texture icon-like thing for the spawn egg. Like the alien vs predator mod, the spawn of the aliens had a custom icon on it.
I also wanted to know how to add a description to the custom entity spawn egg, I'm a beginner to modding.
Yep, like coolAlias said.
Then to add a custom description, override addInformation in your Item class.
See this GitHub for an example of an item that adds a custom description. This specific one supports language translation, but you do not have to do that right away.
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Don't use #findGlobalUniqueEntityId or #registerGlobalEntityId - all you need is EntityRegistry#registerModEntity with your IDs starting at 0 and incrementing.
However, that will prevent you from being able to use the vanilla spawn eggs, which I didn't realize you were wanting to do. Pre-1.8, it's not possible to do without using global entity IDs, and that is not recommended. Instead, you have to create your own custom egg Item like I mentioned in my first reply.