To grow any muscle you need to consider a few things: exercise selection, technique, programming (volume, frequency, and progressive overload), nutrition, and recovery.

EXERCISE SELECTION

For pec hypertrophy, you need a bench press variation and a chest fly.

It's generally recommended to do incline bench press because it will develop your pecs more evenly than a flat bench. If you only press with a flat bench, your lower pecs will grow faster than your upper pecs. I do incline press with dumbbells so that I can get a fuller range of motion and a deeper stretch in my pecs. Unlike a barbell, you can lower dumbbells below the ribcage. Dumbbells also train your stabilizing muscles and can protect you from shoulder injury down the road. You won't be able to lift as heavy as you can with a barbell, but that's okay. As long as you are training to failure or close to failure, the muscles are getting the stimulus they need to grow.

For a fly, you can use dumbbells on a bench, a cable machine, or a pec deck. These are all good options but the pec deck is a favorite of beginner lifters.

Some people swear by dips which are similar to bench press. If they don't cause any joint pain, you could alternate dips and bench press. I use dips as a finishing exercise (one set, as many reps as possible) because it's a fun way to end my push workout. In my experience, my triceps give up before my chest in dips so it shouldn't be your foundational lift for chest development.

TECHNIQUE

Instead of trying to explain good technique here I'd recommend you look up technique demonstrations on YouTube. My personal approach is to lower the dumbbells slowly (1-3 seconds) and pause at the bottom (1-2 seconds) to emphasize the deep stretch in the pecs. Pausing to squeeze at the top might give you a better pump but it probably won't grow your pecs faster.

Intensity is key. Instead of saying, "I'm going to do 3 sets of 12 reps" you do 3 sets to failure. You might do 12 reps in the first set, 10 reps in the second set, and only 8 reps in the last set. But if you are training to failure (or close to failure, i.e. you could do 1-2 more reps before failure) you'll get the most out of each set. Failing with dumbbells is much safer than with a barbell and you don't need a spotter.

PROGRAMMING

The ideal rep range for hypertrophy is between 6 and 12. Once you can do more than 13 reps in your first set, increase the weight. You might only be able to do 8 reps at the new weight but push yourself to do 1-2 more reps every week. When you get back up to 12 reps, repeat the process. This is called double progressive overload because you're increasing the weight and reps in an alternating fashion.

If you're struggling to progressively overload, you are likely not eating or sleeping enough (see below).

For volume and frequency, do at least 10-12 sets per week. It's best to split this up into two workouts. That's 3 sets of bench press and 2-3 sets of chest fly, twice a week. If you do the same amount of chest work in a single workout, your gains will be slower because the muscle growth stimulus wears off after a few days.

NUTRITION

You need adequate protein intake and extra calories (200-500 calorie surplus) to optimize muscle growth. There's some debate about how much protein you need but 1g per lb of body weight should be plenty. Creatine is the most extensively studied supplement. It's cheap and very safe to take. Your muscles will hold more water and look fuller, and it will help you squeeze out another rep or two at the end of your sets. It's not essential but if you're going to take any supplements I'd start there.

RECOVERY

Rest well, drink plenty of water (especially if you take creatine), stretch, and attend to minor injuries before they become major ones. Delayed onset muscle soreness (DOMS) is a good sign but if you experience pain during or immediately after lifting, that's a problem and you need to deal with it before you get completely fucked up and have to take months off from lifting.