This guide will go a bit more in depth on upgrading equipment. I'm going to mainly talk about the "soul stones" that you use to upgrade a weapon that'll give it a glow. In terms of cost, it's actually expensive to upgrade equipment at lower levels, but it slowly becomes easier as you gain levels.
Credit for this guide goes to everyone on these forums because I just gathered info from a few topics and then built off of what I learned from them.
First of all, I'll explain the weapon.

What I labeled as "1" is the amount of sockets the equipment has. The most sockets I have seen is 4, and NPC bought equipment has zero sockets.
Labeled as "2" is the equipment level, not to be confused with the required level to use the piece of equipment. The higher level the weapon is, the higher this number will be.
Sockets is what you put your soul stones into, and depending on how many sockets you have, is how many stones you can put in. The equipment level determines how strong of a soul stone you can put into the piece of equipment. The equipment levels go from 1-15, and there are 12 levels of soul stones. You can't put a higher level soul stone into a lower level equipment, so you can't put in a level 5 soul stone into a level 4 equipment or lower.
Now here's the guide to actually getting, and putting your soul stone into your equipment.
First, find a NPC that sells these items. You can tell what level soul stone it is by just looking at its description, if it's level 1, you'll see that 1 in yellow.

In order to find out how many level one soul stones you need to make a certain level soul stone, refer to the chart on this site
here.
After you have all the level one soul stones you need, find this NPC here and choose the second option.

After choosing the second option, you'll come across this big extensive crafting page. You don't need any kind of crafting levels to do this, and you get 6xp for each soul stone you craft.

After crafting whatever level soul stone you desire, find the respective NPC for whatever type of equipment you're trying to upgrade. (Weapon seller if you want to put them in a weapon, or the armor seller if you want to put them into your armor)

Last, take your weapon/armor and place it in the top slot, and put your soul stone into the bottom slot.
GlowsThis part is not complete yet, but I have partial data on it now and I'll go ahead and blow most of my money on finishing it since I feel like waiting for an English version now.
So far most information about glowing is either wrong, or I don't believe it yet because everything I have learned in the past has been found wrong. I found out that one level 5 soul stones do not give a glow, but multiple will.
You need at least two level 5 soul stones to get a glow in armor. I'm not sure if it works the same with weapons or not yet, as all my information is not complete. I did add a third level 5 soul stone into this armor, and the effect is barely any bigger if it is even bigger at all.


As for weapons, having a three star weapon does give it a small glow.

So it seems that glows work differently for armor and weapons.