First let's look at the two main ways:

A) Replace the screen/glass

1) This is if you broke the glass
2) This does happen
3) Any technician and just the process is more expensive than just getting a new monitor

B) Replacing the whole monitor

1) It's new and untouched, in most cases
2) More cost-effective

To replace a monitor:

1) Pick your budget

NOTE: MOST MONITORS ARE FROM $100-$400, DEPENDING ON BRAND AND SIZE

2) Pick your size
3) Pick your brand

TIP: IF THE BRAND IS MORE IMPORTANT THAN THE SIZE, THEN SOMETIMES YOU WOULD HAVE TO PICK ONE SIZE SMALLER TO STAY IN YOUR BUDGET

4) Pick where you want to purchase it

NOTE: I SUGGEST EITHER BEST BUY, TARGET, EGG.COM,TIGERDIRECT.COM OR EBAY BECAUSE THEY ARE MOST COST EFFECTIVE AND HAVE BETTER CHOICES

NOTE: STAY AWAY FROM CRAIGS LIST
NOTE: STAPLES IS OKAY, IF THE HAVE...

5) When you get it, simply recycle the old one and put the new one in

NOTE: I AM A STRONG SUPPORTER OF RECYCLING WHEN POSSIBLE, SO TRY TO FIND A RECYCLING CENTER OR GIVE IT TOO SOMEONE WHO DOES

Hope that helps!