Skin-to-skin contact really helps with bonding. It's a good idea to have your baby lifted onto you as soon as they're born and before the cord is cut so you can be close to each other straight away.
Either before, or just after the cord is clamped, your baby will be dried and then covered with a towel to stop them getting cold. You can continue to hold and cuddle your baby while this is done.
Your baby may have some of your blood on their skin and perhaps vernix, the greasy white substance that protects your baby's skin in the womb.
If you prefer, you can ask the midwife to dry your baby and wrap them in a blanket before your cuddle.