I am the guy who, if I pull up next to you at a stop light, and I see that your kid is running around in the backseat, I am rolling my window down and will probably shout some obscenities at you. I have no patience for ignorance, especially when it comes to the safety of children.
I became a Child Passenger Safety Seat Technician (yes there is such a thing) about 5 years ago while working at the dealership. I didn't have any children at the time so I thought, how hard could it be to buckle in a car seat. Harder than you think. Since then I have voluntarily instructed parents, grand parents, and anyone else how to properly install car seats and kids into those seats.
You are going to hear me talk about this topic a lot. I am very passionate about this, so my tone in some cases will probably resemble a rant.
Let me start with my first tip:
Keep your infant rear facing for as long as possible. The rule is one year or 20 lbs, which ever comes first; however, rear facing is the absolutely safest position for your child to be in because their head, neck, and back are completely supported in a front end crash. If your child is one year old but only weighs 18 lbs, keep them rear facing. Try to max out the weight limit for the seat, which typically is 22 lbs. Should your child grow to the point where their ears are just about to reach the top of the car seat, then go ahead and put them forward facing. Some parents think their children get bored of looking at the back seat and if they turn them around so they face forward then their children will be happier. Guess what, your kid doesn't know the difference because facing the backseat is all they know! It's you who would feel better if they are facing forward. Keep your kids saftey in mind, not your convenience.
Lastly, for now, always take your car and car seat to your local police or fire station to have it inspected and installed correctly. Maybe later I'll tell you some horror stories of what I've seen new dads resort to in order to install a baby seat.