You can use Nestabilities dies in your Cuttlebug. To cut paper you won't need any special plates, but to emboss, you will need to purchase an embossing mat. You can find instructions for the Cuttlebug on the Spellbinders die compatibility chart here
. You can also find it inside each Nestabilities die package.
To get a deep impression when you emboss, just like you would when using the wizard or the Grand Calibur, I suggest you try using Scor-Pal's new "No More Shims Embossing Mat"