Roll out all the rounds of dough, and stack them with waxed paper or plastic wrap between if you don't have a lot of counter space, and cover with plastic wrap, then a towel to keep from drying out. Then, when you're going to fill them, start with the first one you rolled out, so the dough has rested. Spread the filling thinly, leaving a 3/4-1 inch border on the edges. Roll up like a cigar, pressing out any air, and snake these rolls into a spiral with the outside exposed edge to the inside of the spiral. Again, finish this step with all the rounds of dough before going back to the first, keeping them covered in plastic wrap and a nice heavy towel to keep out air. (Maximum rest time is key!) Start rolling out the spiraled filled dough cigars gently, working them in succession if need be, in stages, so you're never overstretching resistant dough. If they're too resistant, let the gluten relax for half and hour or so before getting them all rolled out. I like the snaky cigar method much better than trying to spread the filling through rolling out a round of dough with filling in the center. Spreading and cigar rolling is much easier, though it does make for a different finished product.
Are you using one piece of dough, putting the filling in the middle, and pinching the top? If so, after you pinch it, flip it upside down so the pinch is on the bottom. As you roll, the filling won't ooze that way. the alternative is to use 2 discs of dough, and roll them together with the filling in the middle.
Also, make sure your filling isn't too course, and don't overstuff the paratha.
Knead the dough really well so it is soft and pliable.
Don't use too much filling.
Keep chopped/mashed/grated small so there are no big chunks to push through.
If you have trouble rolling them out the most normal way (take a portion of dough, make a small circle, put filling in, pull up round filling, roll out), you can also cheat and split each portion of dough into two and roll them out into rounds, then spread filling on one side and put the other on top. This is the cheats method!
With practice you will get better, I promise.
Experience? I say this humbly and playfully.. as I'd love to find the secret too. I'll point out what I've learnt along the way. Some things to avoid:
1. Lumpy filling - say for aloo paratha
2. Very dry filling - more a problem for kachoris than parathas, but may prevent a good seal at the crimped seam. Also a crumbly filling may lead to air getting trapped inside and this will lead to punctured parathas when rolling them out.
3. Too stiff dough - if dough isn't pliable enough, it'll tear. Allow it rest after kneading, before stuffing and rolling. You may want to try adding some all purpose flour to the atta, to help with this.