If you want to customize an amigurumi pattern to match a specific character or pet, I’d advise that you keep it simple and don’t try for a perfect match (see some examples here). Always start by choosing yarn colour(s) that most closely match your pet – that may be all you need to do!
If you want to match your pet’s markings more closely, adapting a pattern to add custom colours can be challenging, but I can offer you some advice to get you started:
The second option isn’t easy – you’ll have to keep detailed notes, and it may take several attempts to modify the pattern to get the right colours in all the right places. I’d recommend you use embellishments to add additional colour details, unless you’re ready for a challenge.
For more guidance, The Essential Guide to Amigurumi covers all these techniques. It’s packed full of instructions for all aspects of amigurumi, including more abstract topics like embellishing and customizing that you won’t find in any other book!