1st rule - don't, don't, don't, breed related dragons. If you intend breeding get your stock from different places at different times. This gives you a more than evens chance that they are unrelated.

2nd rule - wait until they are at least 18 ~ 24 months old.

Assuming that you follow the above and have given you beardies the best you can in the way of microclimate, food etc. then the following should help in breeding.

Best results will be achieved if the beardies are allowed to brumate (see general Care Sheets on Beardies) - a cooling down period provides an impetus to breed. As they wake in the spring start feeding them up, the male will show what appears as aggressive behaviour biting at eye ridges and beard (not my idea of fun but it seems to work). Some damage to the skin may occur, this is not unusual but if it is severe you may need to separate them. Your female should then start eating voraciously - fill her with as much calcium rich food as possible plus all the fruit and veggies she will take, generally spoil her rotten.
My own beardie went approximately 3 weeks after we noticed mating rituals before laying. For 2 ½ weeks she just appeared to be filling out well but in the last few days egg bulges appeared in her abdomen which could also be felt by running your fingers over her gently - she actually looked like a sock full of marbles. In the last two days she started pacing her enclosure and digging frantically.
This is where you need to have made early preparations, unlike us the first time round!
We have a 3ft quarantine tank set up with basic heating and not much else - into this we place her egg laying cave (they do like their privacy). This consists of 2 kitty litter trays the bottom one full of damp coarse vermiculite (or perlite) damp enough that you can mould it by hand. The top tray is clipped onto the bottom and has an oval cut in one end big enough for mum to get through easily - build up your substrata so that she can get straight in to the cave (those of you who have been pregnant will appreciate not having to put to much effort into moving around!). Place her in the tank as soon as you notice her digging and leave her alone. She will dig somewhere in the cave, lay a clutch and then cover them so that it appears that nothing has been disturbed, the only way you will know she's laid is either seeing her do it or the fact that suddenly she is slim again.

You now have two things to deal with - an exhausted female and up to 40 eggs if you're lucky.

1/ If you value her health then stick to 1 ~ 2 clutches a year which means don't return her to an enclosure with the male, they can retain sperm and go for a 2nd clutch (very surprising when not expected). She will need rest and again lots of calcium rich nutritious foods - I would also give her regular spray baths with water containing electrolytes (this is a personal thing).

2/ The eggs - you have of course already warmed your incubator to 28.5C in preparation for the event.

Partly fill a container with the material you have in the laying area then gently locate the clutch of eggs, I've been through the material with a pastry brush and tea spoon slowly and carefully trying to find them. Having made a series of dents in the container material with you thumb transfer the eggs one at a time and rest them in the dents - BE VERY CAREFUL NOT TO CHANGE THE ORIENTATION OF THEM - for whatever reason this is very effective in destroying any chance of a full hatch. The first 24 ~ 48 hrs are critical in development so as little disturbance as possible is required.
We use plastic 2 litre ice cream containers for this with holes punched in the top. These should be placed in the incubator and checked approximately weekly to see that
1/ the vermiculite isn't drying out (if it is CAREFULLY moisten it with a spray)
2/ no eggs have died - usual signs are collapse of the egg or mouldy appearance - if any show this then you can remove them.

At around six weeks you should then visit your bank manager and arrange a loan to purchase the buckets of crickets needed to keep the tribe fed.

Incubators

A simple but very effective incubator may be made by obtaining an old bar fridge, remove the motor etc. so that you effectively have an insulated box with shelves. Fit a simple wall type thermostat connected to a heating globe suspended inside the fridge. Cut a panel out of the door and fit a Perspex insert as a window and also install a simple probe thermometer with the sender near the eggs to monitor the temp.

That's it!!

You will of course ensure that all electrical work is carried out by a licensed electrician following all the statutory regulations which may apply in the area in which you live.