To make a Nostalgic pet you need a Nostalgic Instructions of the pet you want, a Kit, that can be the Plastic Molders, Plushie Makers, Metal Workers or Wood Carvers, depending on which pet you are making, and an Essence of Melody You have to visit Vanya's Workshop with the instructions to start a quest, after completing it he will transform your active pet into a Nostalgic one
I can clarify for you, but one of the items you need is 8 million sPs. Do you have 8 million sPs? You can complete the quest without it, but you will just get a toy. Your pet will not turn nostalgic without it.
OK, great. As stated above, you need to buy the Nostalgic Instructions that goes with your pet that you want to turn Nostalgic. That pet must be your Active pet. If it's a Kumos, for example, the item you'd buy would be Nostalgic Kumos instructions. You also need to get an Essence of Melody. This is what makes your pet nostalgic. Once you have both in your inventory. you can go to Vanya's Workshop where you have to do a quest in order to turn your pet nostalgic. You will then have to get a few items and once you're done, your active pet will turn nostalgic.
Above information is a little off. You basically need the Nostalgic toy of the pet you want to be nostalgic. You can either make it with the Nostalgic instructions (+ a few other things that Vanya will tell you to get) or buy the toy straight from user shops. THEN you take that toy to Vanya with your Essence of Melody to turn YOUR ACTIVE PET Nostalgic. That's very important. He will make whatever pet that is currently active on your account into the pet toy you gave him. If you want to make a new pet and turn that nostalgic, make sure you make it active before going to see Vanya, or you're gonna be out a bit of monies. :p
Also, if you've been visiting Melody's cottage every day so far, you'll get the Essence at the end of the month if you visit all 31 days. :)