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Ordinarily supply is produced somewhere, usually in locations, that is things on the map (ie. cities).

Since supply is produced, like any other item (ie. tanks), then they need to be connected to an HQ.

This is done by selecting the location (city or whatever), and then clicking on the button on the lower menu line that looks like a factory with the text HQ on it. Then you select the HQ, that you want to get production from this location, and press the OK button.
Note that the cities in this case are shown in a green highlight. They may not be in your game, but, you can turn this on in the preferences.(The computer symbol, that allows you to save as well. There is a menu point called Preferences, and then a Box you can click to put a check mark in, called Show Location Bases.)

To produce supplies (or anything), you need to set it. This is done by selecting the Factory "button" from the lower line, that has no symbol on it. You have to have selected a Location hex that can produce for it to be available. It will bring up a menu in the lower half of the screen, where you have 4 production lines.
Here you can select a menu type, in the first column and after that, an item type (of which PPs & Supplies in this case, are part of the Non-Combat menu). The numbers that can be adjusted (10, 20, 30..., 100) represent the production percentage of the location used to make that kind of production.

Note you need to Press "Select" to change or set the production from what it is (or perhaps there is nothing being produced in that production line...)

Now that we have gotten production of the supply sorted, and sent it to an HQ, it is time to understand the different levels of HQs.

HQs are arranged in chains. They connect to each other. Each HQ can connect to only one HQ, but multiple HQs can connect to an HQ that connects to others.

That is, several HQs can be subordinate to one HQ.

Units can either be subordinate to an HQ, or not to anything at all. The same goes for HQs, so units cannot be commanding other Units or HQs.

When a Unit asks for Supplies, it will get them from its parent HQ, if that doesn't have enough, it will request from it's parent HQ, if it has one, etc. There is a maximum amount of HQs that can be in a chain this way, so be aware of this. Think of it as Corps command connects to Army Command, connects to the overall HQ.

An HQ has a maximum range, which it can send out Supplies to. This is determined by the amount of Action Points it takes to get to that place. Supply travels best along roads/rails, and worst through places like mountains without roads/rails.

Now, it would be alot to ask players to count the hexes that the supply could travel, so while you probably could do that... I wouldn't want to... you can get some information from the Supply Overlay button.

It is accessed by pressing the Button on the lower menu, that has a Jerry can on it (fuel can if you will). You will need to select the HQ you are testing where the supply can go to for it to tell you though.

When you do, the following shows up (on the scenario map I chose).
Note the different colors, and the lack of any color. The lack of any color means, that it is impossible for supply to get there. This is the case for ALL enemy hexes (this will change once taken). The RED overlay color will tell you that only 25% of the supply will arrive there, the Teal(?) colored hexes will show that only 50% of supply gets there, and the Yellow will tell you that 75% of the supply gets there... The Green hexes are where supply will arrive without any penalty to the amount.
Note you can choose a hex (like I've done here). It is shown as a hex with a grey outside highlight, instead of the black hex border. The RED arrows here show how the supply is flowing there. If that flow is disrupted, by being conquered, then it will of course travel in another way...

Now turn off the Supply layer. We don't need to use it any more, point has been made.

If you now go to a unit (or HQ even)...

You will see something like the following:
The numbers below the counter show here are

Sup. Cons. (Supply consumption, how much it should expect to get, % of needed), Sup. Stock (Supply Stock, how much it is already carrying, usually double the amount needed for consumption = 100%, if it has all it can carry). Req. In. (Requested In, the amount that it wants to have last turn), Sup. In (Supply in, the amount of supplies it got from it's parent HQ). Supp. (Ask for Supply amount, set in percentage. You can set it lower if you think you are running out and want some units to have less, rarely used).

A small dot on the unit (on the map) will show how much supply it got/has of needed. If it is red, it means that supply status is critical, if yellow, low, and if green, everything is ok.

I lack describing how you know that you are producing enough supplies.

Here is a short overview.

You start by selecting the Button where you see a factory, and the text "Over" written on top of it.

This will bring you to a screen that looks somewhat like this:
On the right hand side you will see a lot of numbers, next to some text, in the Box called "Total Production".

Here when it comes to supplies, there are 3 important lines. The first one is "Total Supplies Required". A somewhat misleading (I've found) estimate of how much supply you need. The second line you see is "Supply". This is the ACTUAL amount of supplies you are producing, for that HQ.
Notice how these numbers change when selecting an HQ from the List in the "Headquarters" list box. I've chosen "Shanxi Clique HQ", and it has a redhued background. You can click on any of the HQs listed there, like I did to get up the specific information for that HQ.

The "Total Production" Box from before has now changed a bit. There is the line "Last Supply Req." and then a number there. This is the amount of supplies that the units below the HQ have requested the last turn. The there is the "Supplies needed by HQ" which tells you how much supply the HQ will need this turn. Note: This number can change as units that are bought do come in with some supplies, but will of course need some more down the line. Finally there is the "Supply" text, that says how much supply is being produced by this HQ.

Now in this case I could be asking for trouble, only having produced 2667 supplies while asking for 11005. However the HQ is connected to another HQ that is it's parent, so it will draw the additional needed from there.

You will also note that there is a Line in the Headquarters box that says, "No HQ". It can be a really good idea to select that at times to see what Locations (cities etc.) that DON'T have a HQ connected to them, and thus are not producing because of it.