How To Tune A Piano and why…
I would like to first state that tuning a piano does not require a master's degree in knowledge past down from the noble tuners of the 1800s royal family bloodline.
With a quick Google you've probably been put in shock by people who say things like...it's a skilled craft...or maybe damaging the pins could cost more money...or hell maybe you don't have the ear or precision required. These are written by piano tuners that do this for a living (or rich people who can afford a tuner lol). While they do have skills for actual piano repair that does require craftsmanship...tuning is not one of them.
The cost of tuning will be hundreds of dollars, plus if it's really out of tune they will have to come back for multiple visits. The alternative is a $30-50 tuning kit and a day of your time. My first tune took me 7 hours, BUT DON'T GET STRESSED OUT!! The process is easy, but it gets reapplied to 230 strings. Definitely not hard, just tedious.
Calm your shaky hands with these
Misconception 1 - damaging the pins that hold the strings. This is where you will tune it.
This one's kind of funny once I explain it. Each string holds about 168 pounds, making a standard piano's entire string tension about 18-20 tons. That's about the weight of two average size elephants. Seriously, Google it lol Long story short, the pins aren't brittle.

Can you damage pins at all then? Yes. When turning the tuning hammer make sure it's fully on the pin and your moving it up/down, not diagonal. Obviously sometimes you might accidentally, just don't make it a habit. We're not trying to prove me wrong xD
Misconception 2 - You need 'the ear' and the skill.
Not really. We will talk about a meter in this article that will remove your ear all together. When it comes to skill, remember small movements are king. You will be a master of this on string 157. I promise.

Misconception 3 - you need expensive tools.
Nope. Like I said, a really good tuning kit is going to run you $30-$50 on Amazon. Just make sure it has the tuning hammer, a couple wedges, a felt strip, and for bonus maybe a tapping hammer for slightly lose pins.
$35 Tuning kit I personally use

Source: Amazon.com
Let's get started!! :)
WARNING!! Please do not use a wrench, pliers or any hardware store tools on your precious piano. If your a handy man like me than you know this is your first instinct. It's not worth it. The tuning hammer will 100% make sure you are moving the pin correctly. Damaging a pin will require a professional. Let's not risk that over $50.
STEP 1: Get an app that can check the levels. I think PianoMeter is a solid app. If you have an actual meter, that's cool too.
STEP 2: Each string has to be isolated. Notice the middle keys have 3 strings per key. Use your felt strip or wedge to jam the two that your not currently tuning.

2nd example so you can interpret my crappy drawing lol

source:HowToTunePianos.com
My personal preference is to felt strip one string section at a time unlike the 2nd example. I feel it's too easy to forget what strings you did and didn't do.
STEP 3: make sure the tuning hammer is all the way on.

STEP 4: Set your meter up and press a key down with no pedals pressed. Hold the key until the sound begins to lower. The sound your looking for is the in-between sound. This will give you the most accurate reading. View example to get the idea.
Key strike audio wave example:

Notice that the initial key strike is too strong, while holding too long will weaken in volume. It's fine to over hold, just re-strike if the volume starts to drop a noticable amount.
STEP 5: Watch the meter. Your goal is to have it hit as close to zero (middle) as possible. You may not get it 100%, but aim for -3 or +3.
Now if the meter goes to the negative or left, tune the hammer right. If it goes to the positive or right, tune it left.

STEP 6: This is really just an expansion on 5, but make sure you are moving the hammer perfectly up and down (upright piano) or side to side (grand piano). No diagonal or other weird movements. This can damage a pin if done intensely.
**Pro Tip**: Do small movements, less is more. The weight of a couple pennies can tune it pretty far. So dial it in, then to get it closer to zero...move it like a feather.
Let's finish this bad boy off!!
Now just repeat those steps until the entire piano is sounding beautiful. You may have to do this in a couple weeks again if your piano was really out of tune. This is due to the fact that the metal base that holds the strings has expanded. Your goal is to re-warp that so it can hold a perfect tune. After that a tune or two a year will be all it needs.
So enjoy the process and go save that money $$$
If you want to listen to some of my in-tune piano songs Click Here :)