I'm going to make this short guide for people to explain Modding Skill Trees. It's relatively simple although there are some issues that you may run into.
First off I'd like to point out that it has nothing to do with adding Skill Points. The game has a sanity check on how many Skill Points you should have regardless of what you put in Gibbed, so you can not do it that way.

First you need to open your save up in Gibbed and go over to the Raw tab and scroll down to SkillData.

[ Register or Signin to view external links. ]

Click the down arrow on the right to open a new window.

What you'll now see is list of SkillData values in the window on the left side. These correspond with each skill on your Skill Tree (there are a few exceptions that I will cover in a moment).
When you click on one you will see the actual skill in the window on the right and a Grade value. The first value in the SkillData list is your actual Action Skill itself (Gunzerking, Phaselock, etc), so this Grade will always be 1.

[ Register or Signin to view external links. ]

Change the Grade to the appropriate value.

If you are unsure of the Grade value for a particular skill, you can just set them all to 5 and the game will auto-correct it on load. It will not allow you to set a value higher than what is possible in game.
If you are like me and detail-oriented you can reference the Skill Calculator to know what values are 5 and which are 1.

BL2 Skill Calculator

Now, we'll get to the exceptions in the SkillData values. The 2 DLC characters have some items in their SkillData sets that do not directly apply to skills in their Skill Tree.
These are not to be modded or it will cause issues in game. These are the values that you want to leave alone:

Mechromancer
GD_Tulip_Mechromancer_Skills.LittleBigTrouble.LightningStrike

Psycho
GD_Lilac_Skills_Bloodlust.Skills._Bloodlust
GD_Lilac_Skills_Hellborn.Skills.FireStatusDetector
GD_Lilac_Skills_Hellborn.Skills.AppliedStatusEffectListener