I strongly recommend that you complete your adoption through a licensed agency. You may be required to spend weeks in Russia if you do not.
Once you have your documents notarized, they will then need to be apostilled. An apostille is basically a notary of a notary. Russia will only accept your original documents in BLUE ink, this includes notaries and apostilles.
You should, whenever possible, hand carry notarized documents needing to be apostilled to your Secretary of State's Office.
When purchasing your airline tickets, you should strongly consider paying (sometimes more) for the adoption rate. This allows for less of a penalty if you have to change your flights.
When you purchase your visas, purchase travel visas as opposed to business visas. Embassy requirements are always changing so be sure to be up to date on their most recent mandates.
Use a money belt to securely carry your cash, passports and other valuables.
You may want to think of a comfort item you can leave with your new baby while you travel back home to await a court date. We gave each of our children a pillow with a picture of their new family on it.
Be generous with orphanage donations! They need everything!
Take a lot of pictures and video during your time with your baby. Take in the sights and feel of the orphanage and of the city; it's an invaluable gift to later share with your child. And, your reflection will keep you sane until you get to hold your baby again.
Stay busy getting the nursery ready while you are awaiting the second invitation to go back to Russia for court.
Once you are finally home, you should immediately apply for the child's social security number. This can take a number of weeks and is necessary to have for many reasons.