The classic way to make a caramel sauce is to cook approx (this is what we use at the restaurant, because sometimes we get distracted and have to run away; it's more forgiving. Use less water if you can concentrate) 4:1 sugar:water until the sugar has taken a golden colour. Remove from heat, whisk in cream and butter until you reach your desired consistency, add a pinch or two of salt, just enough so you can taste it. This will get you a nice caramel sauce, keeps a week or so at room temp.
Edited to respond to question:
Honestly, I have no idea what the ideal ratio is. I just do it by feel. There should be a zillion caramel recipes available via google that can be more specific. Offhand I would kind of sort of guess that for three cups sugar I use roughly 3/4c cream and 3tbsp butter. Ish.
Edited to provide another answer:
If you wish to use condensed milk to create something that will be closer to a dulce de leche, do the following. This can be extremely dangerous, please be sure to follow all directions. I am not responsible if you injure yourself:
Fill a large pot with water. Keep another pot boiling for topping off the main pot as water evaporates.
Place a can of condensed milk, still sealed, label removed, into the main pot. Bring up to a hard rolling boil. Top up the water as needed. Ensure that the can is always covered with at least six inches of water. Keep a lid on the pot, just in case.
Boil hard for four hours. Turn off the heat, and allow the water in the pot to come slowly down to room temperature. Do not at this point touch the can.
After cooling, let the pot continue to sit at room temperature for at least one hour. At this point, reach into the pot and gently touch the can with your hand. If it is still warm, leave it to cool further.
Once the can is completely cooled to room temperature, you may open it. If you want to be sure, leave it overnight.
You will have a glorious caramel sauce.
Note: I have intentionally described this process with significant margin for error for safety. There will be significant pressure inside the can, and opening it prematurely can very easily result in life-altering injuries.
Walk away.
No, really - it works. Once you add the water to the sugar, it will likely harden and clump up (I don't know how to stop that happening). But once it does, you can just walk away, and leave it to sit till it cools down.
A lot of the sugar will just dissolve on its own, given time and enough water to dissolve into. Some mixing (occasional stirs as or after it cools) will dissolve some more. And at the last, when most of it has dissolved, you can gently start heating the pan up again, stir it around, maybe bring it to a boil for a bit, maybe add a bit more water and heat some more to get at those last undissolved chunks...
It's sugar, in water. It will dissolve until the water's saturated. It takes time to dissolve on its own, and that's annoying if you want to use it right away - hence measures like heating, or stirring, or crushing the dried caramel to stir into water that way. But it really works just as well, and is less tedious, just to give it some of that time and let it dissolve away.
I did this when making a caramelized burnt-sugar syrup, and it worked. Adding the water was pretty spluttery at first (the caramelization had to be stopped pretty fast), but I did notice the caramel hardening to the bottom of the pot once it had settled a bit. I gave it a few stirs, and walked away to take care of something else - and by the time I got back to it, most of the lumps were well on their way to dissolving.
Best Answer
When caramelizing sugar in a recipe that uses water your first job is to get the sugar to completely dissolve. That is the first temperature you are using. They are probably making you pause at this temperature long enough to make sure you do this tep correctly. If they didn't have the step most folks would blow past it, add more ingredients and run the risk of not dissolving the sugar correctly.
Make sure no sugar crystals remains at the first stage, even on the side of the pot. If any crystals remain or fall in later your recipe will fail because the sugar will recrystallize leaving a grainy taste.