I know how hard it is to find time to exercise when you're a new mom. The first twelve weeks, you don't need to be going full force anyways because you could severely injure yourself.
Start with some squats. You can hold your baby anyway you'd like. Keep your back straight and your legs parallel to your shoulders. Inhale as you squat down, exhale as you come up. Make it fun by counting with your baby or singing as you squat. This helps the baby have a good time too. Start with maybe five or ten if you're just getting started.
Back lunges are a great way to tone your legs. Bend your right knee and step out on your right foot, keeping your upper body straight. Your left leg should be extended behind you, foot forward and knee straight. Again, hold your baby in whichever position is most comfortable for you.
After being stretched out for nine months, you definitely want to focus on your core. Lie your baby on the floor on a blanket. Get in the push up (or pike) position, with your elbows and lower arms are on each side of the baby, with your legs straight out and on your toes. Make sure not to drop your back down low. Hold yourself in this position for about 90 seconds. Repeat five times. While in the pike position, try some push ups, kissing your baby every time you drop down.