Ok, your house was built in the 50's or 60's, before anybody got creative with texturing walls and ceilings.
The walls of your house have probably been skip troweled, and you want the room or wall you are working on to match the rest of the walls in the house.
First let's define what the texture looks like: Random flat modeling or (Islands)in varying sizes with low flat spots (That's the drywall)and it looks like it has sand in it. After 40 years of paint layers, it also displays a bit of an orangepeel texture, from the little bumps that the paint roller leaves behind.
1 or 2, 5 gallon buckets of water.
12" Stainless Steel Mud Tray.
12" Stainless Steel Concrete Trowel. (Dont use regular steel or the blue coated trowels. They rust while using or sitting in bucket of water, and it transfers to your walls.)
Beach sand or Supreme 30 Mesh. (30 Mesh sand has larger rocks in it.)
Use about a half cup of sand or a little more mixed into a 5 gallon bucket of mud.(This is strictly dependant upon how much sand you want to see on the wall.)
After mixing the mud,(leave mud thick, you can always thin later if needed.) fill your tray same as you would when taping seams. Take your concrete trowel and scoop some mud on the top edge of the trowel. With the mud on the top edge of the trowel held about 4 or 6 inches away from the wall. Snap the trowel with your wrist toward the wall.(like flicking your finger)The mud will fly off and create a random glob/globs on the wall. Smash it flat and swipe it left or right in the same motion. You will notice some buildup on the bottom of your trowel after a while. Don't clean it on the edge of your mud tray. Clean it off on the wall first. Edges and corners are a little harder when trying to flick the trowel. I use a 1x4 about 8 inches long with the edge dipped in the mud, then glob it on the wall and swipe it flat with the trowel. (But you can use just about anything to get the mud on the wall.) Depending how the modeling looks on the wall in some areas, I will sometimes stick 4 fingers in the mud and flick them on the wall. The buckets of water are for your tools, keep them wet and submersed in the bucket when you need to break. Get used to using the drywall sponge. Read the instructions on any bag or bucket of mud. They specifically state. Avoid sanding if possible. It is so much cleaner.