Eating should still be predominantly breastmilk or formula. It is very tempting at this age to introduce solids; but unless directed by your Pediatrician, I would suggest waiting. Most babies are still needing to wake 1-3 times at night to feed and that is normal at this age. There are also studies showing that feeding them food such as rice cereal does not make them sleep better and in many cases they sleep worse. They should be getting at least 5-6 breastfeeding sessions per day or 2 1/2 ounces formula for each pound of weight (approx. 20-30 ounces) .
4 Months is a really great time. You will start to see a lot of changes in your little one. Their circadian rhythm will start to develop more and they will be staying up for longer periods of time. From age four to seven months, the most important changes take place within your child. This is the period when they will learn to coordinate their emerging perceptive abilities (the use of senses like vision, touch, and hearing) and their motor abilities like: grasping, rolling over, sitting up, and possibly even crawling.
Their schedule is still very loose and you should be flexible while trying to encourage healthy sleep patterns. You might notice that they are waking more often and taking really short naps and that is ok. Most attribute this to the "3/4 month sleep regression". Which in short means your baby is healthy and developmentally on track.
4 Month Sample Schedule
Wake Time: 1.25-1.75 hours
This schedule assumes baby can stay up 1 hour 15 minutes before needing to sleep again. At this age, wake-time should be 2 hours TOPS, to avoid baby getting overtired.
6:30 – Wake and Breast milk or Formula
7:15 – Breakfast
7:45 – Nap
8:15-8:45 – Breast milk or Formula
9:45 – 10:00 – Nap
10:45 – 11:15 – Breast milk or Formula
11:45 – 12:00 – Nap
1:15 – 1:45 – Breast milk or Formula
2:00 – Nap
3:45 – 4:15 – Breast milk or Formula
4:45 – Nap
5:45 – Begin bedtime routine
6:00 – Breast milk or Formula
6:15 – Bedtime (Goal to be asleep at this time)
+Plus probably 1-3 nighttime feedings
Note: This schedule follows the eat-play-sleep routine. However, it is sometimes hard to do at this age when the amount of time between naps is not long enough.