I have a rifle that has a matte blue finish on it. I like how it is not very reflective. I just wanted to know is there a special process or do they just polish the steel to a satin finish then blue?

After they get the metal where it looks right, it is bead blasted and then blued. The more coarse the abrasive, the more dull the finish. The metal prep usually determines the finished appearance.

Malm

What about sandblasting with a fine sand? Would it leave pits?

I would think that a fine sand type abrasive would produce a nice soft egg shell type finish. I don't know.

Malm

You can etch the surface after polishing with Nitric acid 10 % .

Daniel

Getting a matte blue, I know of two ways :

One is like said, prep the surface, the surface is satin, and so will the finish.

The second is to use "slow-rust" blueing method, the toughest, nicest looking blueing available.
Slow rust blueing is a lot like woman putting on makeups : It must be done by hand, there's many layers and it takes a long time, so it's more pricy. I remember sometime in the past a member posted a picture of a bottom metal with slow-rust finish...looks mmm,mmm, good.

What is the rifle? Maybe it's an early era rifle, at around WW2, that has slow-rust applied to it and only slow rust will match it.

Pyrotek

Matte blue looks nice, but I haven't found it to be very durable. I had one done that way, and the floorplate developed a silvered look, with blue remaining in the tiny pits, after 3 range sessions with suede bags. The matte was achieved by bead blasting. Sand blasting reportedly gives a rougher surface.

I have lately taken to bluing my own with an express blue formulation, and get a nice dark blue/black which is naturally matte. I recently tried as Daniel M suggested and I had previously threatened, and 'pre-etched' the hand polished metal surface with naval jelly for a few minutes, then carefully washing off with lots of water. It took a nice blue in fewer passes as I hoped it would, and had the same matte appearance.
Getting set up to express blue will require a clean water source (I use distilled), something large enough to hold your barrelled action that is heat-proof (I use a $10 large metal flowerbox), heat source, and the bluing product from Brownells.

Todd