Mamiela, those are Magpul M-Lok or Moe rails. Short Picatinny rails 2 or 3 inches long, bolted thru the stock fore end. The rails are polymer, plenty strong but don't weigh much.
You can also get the rails in metal but they are double the price.
You have just enough room with a synthetic stock for the flat T-Nuts that Magpul provides to clear the space between the inside of stock and heat shield.
( On a wood stock Mini there is no space between the stock and heat liner, so on those you have to countersink the T-Nuts ).
Place the rail where you want it, mark where the bolts will go with a marker, and then drill holes slightly larger than the bolt size. Bolt the rail on and you are done. I'd put some Blue Locktite on the threads as well.
The rear swivel needs to be on top of the stock. If it is on the side, like the front, the Mini will want to roll away from you when carried.
And leaving the rear swivel location on the bottom as in the factory configuration would be bad, the Mini would really want to roll to the side.
For a synthetic stock you unscrew the rubber butt pad and take it off, position the swivel, drill holes, and secure the nuts inside. I used some needle nose pliers to hold the nuts while I tightened the screws. For the rear swivel on a wood stock, just replace the supplied bolts with black wood screws.
On an older style wood stock, you can replace the top butt plate screw with the swivel, no need to drill holes) :
The factory bottom mounted swivel position is really limited as far as carry. You can put the rifle across your back if you need both hands free, but that 20 or 30 round mag in the Mini will be digging into your back. And a rifle slung on your shoulder isn't very fast to get into action. And a rifle carried muzzle up on your shoulder will whack low hanging branches.
Maybe it's my Army training but side carry makes a lot more sense. Across your chest in the ready position, it is very quick to bring up and shoot. If you have to drag something or otherwise need both hands free, you can sling the Mini across your back and that mag won't be digging into your back. If you run your rifle dry or there is a malfunction, just let it drop down and draw your handgun. 1.3 Million active duty military personnel carry their weapons the same way:
Some will say "it's just a Mini, and I'm not planning to go into combat".
I doubt I'll be going into combat again at age 62, I carry this way because it's more practical and much more versatile than bottom carry.
Should you want to carry the Mini casually over your shoulder, you can still do that with the side mount system, plus so much more.
My daughter's mini is set up the same way:
Putting a rail on both sides makes sense, you can use the rail on the off side for mounting a light. The rails, flashlight clamp, and flash light (Surefire 6P or G2X Pro Dual Output) are all polymer, tough and inexpensive but lightweight.
Your fingers of your support hand are right there to press the end cap to turn the light on or off.
I've never had any use for a bipod (except for shooting small rodents at long range) but you could also mount a rail on the bottom of the stock for that purpose.
On the Choate pistol grip stock in one of the above pics, I had a Tango Down forward grip on the bottom rail, that grip felt good along with the stock's pistol grip.
This is the Magpul part I use to secure the sling to the rail. They are not cheap but they are Melonite coated steel and have dual release buttons to prevent accidental release.
Cheaper rail mount swivels can be had as well.
You could also forego the rail mount, and just mount a swivel directly without the rail, like these Magpuls, but having the rail gives you more options.