I change the oil on my 2015 Mazda 3 myself, about twice a year. I am self-taught, so this is how I do it and how I learned it. If you have been paying someone else for this, it is one of the easiest first jobs to learn on your own car.
This is the full, step-by-step version. It covers the third generation Mazda 3, the 2014 to 2018 model years.
First: which engine do you have?
This matters more on the Mazda 3 than on almost anything else I work on, because it was sold with two engines. The i trims have the 2.0L, the s trims have the 2.5L. Mine is the 2.0L.
Same oil, same filter, same process. The only thing that changes is how much oil goes in, and that is exactly the number you do not want to guess.
- 2.0L: 4.4 US quarts (4.2 L) with a filter change
- 2.5L: 4.8 US quarts (4.5 L) with a filter change
Quick correction while we are here: in the video I say six quarts. That is my RV brain talking. The 2.0L takes 4.4.
What you need

- 0W-20 oil. Check your manual, but that is the spec, all year.
- Oil filter, Mazda
1WPE-14-302(supersedesPE01-14-302). The Mazda 6 uses the exact same one. - A filter cap wrench that fits the filter (65/67mm, 14 flutes). I find these more reliable than any other filter tool I have tried.
- The right tool for your drain plug. The original plug is a hex (Allen) style. Mine is now a 19mm bolt that Mazda sent me as a replacement, and I like it better.
- A new crush washer for the drain plug.
- A drain pan, or any big open bucket, as long as it fits under the car.
- Ramps, and wood or wheel chocks for behind the wheels.
- A funnel. Mine has swap-in plugs that fit the fill hole on Mazda, Ford and Volvo.
- Gloves and rags. A creeper is not required, but it is nice.
When you are done, take the used oil to an auto parts store. Most of them take it.
Get it up and warm

Line the ramps up so each wheel is centered on its ramp. Start the car, let it warm up a little, and drive up. Warm oil drains faster and takes more of the gunk with it.
Parking brake on, and chock the back wheels. Wood, a wheel chock, whatever you have. You do not want the car rolling back with you under it.
Under the hood first

Pop the hood. The dipstick and the oil fill cap are both easy to find. Take the fill cap off before you drain. Letting air in the top makes the oil come out the bottom faster.
If you use a funnel with a sealing plug like mine, keep its air vent open when you fill later. Otherwise it backs up and overflows onto the ground.
Check the new filter before you start

Look at your new filter and make sure the rubber gasket is actually on it. I have gotten filters without one. Without that gasket it will leak.
Getting underneath
There is plastic under the car that covers the drain plug and the filter. On my Mazda 3, you take out two screws and then pop out a few automotive clips with a flathead. One of the panels gets you to the drain plug and the filter. You do not need the other one.

Those clips get brittle. I broke one doing this video, so it is worth having a couple of spares.
While you are under there, look for oil where it should not be. Seepage around the filter, oil residue on the plastic cover. Mine was just dirty, not oily, which told me my crush washer was still doing its job.
Drain it

Glove up. The oil is hot because the car was running. Get the pan under the drain plug, crack the bolt loose with the tool, then finish by hand and pull it out.
Let it drain until it is just dripping, then give it another minute or two.
Put a new crush washer on the bolt every time. I do not always, and I should. This time I had the part, so I did.
Thread the bolt in by hand until you cannot turn it anymore, then give it a short tug with the socket. That is the amount I have always used. If you want a number, the torque spec is 23 to 30 ft-lbs.
The filter
Keep the pan close, because the filter drips too. Loosen it with the cap wrench, spin it off, and let it drain.

Coat the rubber seal on the new filter with a little oil. Your oily glove works fine.
There are two camps on this next part. Some people fill the new filter with oil before it goes on, some put it on empty and let the engine fill it. Do your own research. I fill mine.
Hand-tight first, until you cannot turn it anymore. Then a little more with the filter wrench.
Then wipe everything clean. A clean engine means that next time you are under there, any oil you see is new, and you know you have a leak.
Fill it and check it

I pull the engine cover off because the funnel fits better without it.
Do not dump it all in at once. I fill about halfway, then go look underneath for leaks. Then I keep going and check the dipstick before the last of it, so I do not end up overfilling.

On the Mazda dipstick there are two little holes. Your level should sit between them.
The car is sitting at an angle on the ramps, so that reading is only a rough one. Get it close enough that it is safe to move, then check again on flat ground. If the engine just ran, give it about ten minutes to settle before you trust the stick.
Reset the oil reminder

Start the car. No oil light is a good sign. Once the screen boots up, go to Applications, then Maintenance, then Oil Change, and hit Reset. Mine is back to 5,000 miles.
The next couple of days
Drive it for a day or two, then check again. Look under the car, look where you park for spots, and check the dipstick. You want to know it is not leaking and the car is not eating oil.
That is it. If there is something you do differently, tell me in the comments. This is how I learned it.
Have a Mazda 6? Same filter, same oil, a little different. Here is my Mazda 6 oil change.