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{Index}
Augment - The act of placing an Augmentor on a tool or piece of combat equipment for the purpose of giving it perk slots and levelling the item/Invention
Dissassemble - Breaking items down into their components, by dragging them onto the lightbulb at the bottom of your inventory, grants XP
Siphon - Using an Item siphon on an augmented piece of equipment will yield XP equivalent to 2 levels lower than if you'd disassembled, but retaining both the Augmentor and Item, but resetting it's level
Components - The building block items placed in your invention pouch for creating Invention items and perks

{TL;DR}
Cheaply + slow
1-4: Invention tutorial in the Invention guild north of Falador

4-27: The most effective method would be to Augment 3 black salamanders then level them to 5, then DISASSEMBLE

27-60: Augment your permanent/staple weaponry and using equipment SIPHONS to get the xp once the item reaches level 12 and go fishing with a fishing rod-o-matic, DISASSEMBLING the rod when it hits level 10

60+: Keep going with fishing rods but augment all possible combat gear for SIPHONING

Expensive + fast
1-4: Invention tutorial in the Invention guild north of Falador

4-27: The most effective method would be to Augment 3 black salamanders then level them to 5, then DISASSEMBLE

27-60: Augment all your equipment and DISASSEMBLE to get the xp once the item reaches level 10 and go fishing with a fishing rod-o-matic or augmenting a crystal tool, DISASSEMBLING the rod when it hits level 10

60+: Keep going with fishing rods but augment all possible combat gear for DISASSEMBLY

{Leveling guide}

1-4: Invention tutorial in the Invention guild north of Falador

4-27: Buy 3 Black salamanders and approximately 1000 ammo for them (or craft the ammo yourself for reduced costs), Augment each of them and level them to 5 on a higher leveled mob that you can kill efficiently, such as Waterfiends, Dark Beasts and Abyssal Demons. Once each of them reaches 5, we disassemble them for maximum XP.

27-60: We can now level our items to 10 and with that, massively increased xp rates. What also comes along is the Siphon, an item that reduces the xp you get from a leveled item by 2 levels, but allows you to retain the equipment and its augmentations.
You can either choose to go the expensive but quick route of disassembling gear, bearing in mind the higher the level of the item, the more xp it grants, so the better the item, the more xp it gives out and by virtue of it doing higher dps, will level faster too.
However, at orders of magnitude cheaper, we can siphon these items, but taking an xp penalty as the repercussion. Any reasonable player would prefer this method unless they have a bank with a surplus of a few hundred million.

60+: Now we have the ability to level equipment up to 15, however xp is limited to level 10, meaning for disassembling, nothing has changed, level the equipment to 10, break it down.
For siphoning however, we will now be leveling to 12, rather than 10, due to the -2 levels mechanic, we can now get the full xp from siphoning an item. The cost of this being that the leveling process for invention is exponential, meaning, while it is more xp efficient to siphon at level 10, it is going to take longer, but the gp/xp has declined dramatically and leveling Invention also becomes more passive

{Things you will be making}


Table from runescape.wikia.com/wiki/Augmentor
depicting how much energy of each type is required, prices from 19/06/2018

Augmentor
Divine energy: 100–2,000
Base parts: 45
Flexible parts: 45
Tensile parts: 45
Enhancing components: 8
Powerful components: 7

Equipment Siphon
Simple parts: 50
Dextrous components: 5
Precious components: 5

Divine Charges
Divine energy: 100–2,000
Simple parts: 20

{Uses of invention}
Useful skilling outfits – Fishing, Runecafting, Mining…

Great skilling tools – fishing rod-o-matic, pyro-matic, augmenting existing tools to make them more effective…

Machines – Automatic High-alching, Hide tanning, Plank maker

Bits and pieces – portable fairy ring, alchemical onyx, herb protector…

Augmentation of gear (perks) – increases dps and survivability amongst other niches uses, more on that in the next section.

{Perks}

Source: rs3bossschool.com/articles/optimal-invention-perks/

Standard Perk Combinations

Weapons
Mainhand: Aftershock 3
Offhand: Precise 5
Offhand (switch): Flanking 3
Defender: Precise 5

Armor
Body: Crackling 3 + X & Biting 3
Legs: Impatient 3 & Enhanced Devoted 3

Other
Cywir wand: Aftershock 1-2 + Planted Feet
Sunspear/Dark bow: Aftershock 1-2 + Planted Feet & Mobile + Reflexes (on Dark bow)
Spirit shield: Absorbative 2 + Mobile OR Absorbative 3
RotS shield: Turtling 3
Enhanced Excalibur: Wise 2-3 + Mobile OR Wise 3 OR Mobile
Corrupted defender: Lucky 4-5 + Mobile

Absolute Best Perk Combinations

Weapons

Mainhand: Aftershock 3 + X
Offhand: Precise 4 + Equilibrium 2
Offhand (switches): Caroming 3/Flanking 3/Lunging 3
Defender: Precise 4 + Equilibrium 2

Armor
Body: Crackling 3 + X & Biting 3
Legs: Impatient 3 + X & Enhanced Devoted 3
Body (Crackling Switch): Clear Headed 2-3 + Reflexes & Lucky 5

Other
Shadow glaive/Cywir wand: Aftershock 1-2 + Planted Feet
Sunspear/Strykebow: Aftershock 1-2 + Planted Feet & Mobile + Reflexes (on strykebow)
Spirit shield: Absorbative 2 + Mobile OR Absorbative 3
RotS shield: Turtling 3
Enhanced Excalibur: Wise 3 + Mobile
Corrupted defender: Lucky 4-5 + Mobile

{Best case materials cost for 99 Invention}

Information sourced from runescape.wikia.com/wiki/Invention_training

It is recommended to obtain Ascended components or Shifting components for Efficient 3 perks for lower costs

Siphoning is slower than Disassembling, but orders of magnitude cheaper.

If siphoning (T90):

A weapon set, body armour, leg armour, 3 augmentors assuming 2H and either -
67 equipment siphons & 278 divine charges.

Or

135 Base parts, 135 Tensile parts, 135 Flexible parts, 24 Enhancing components, 21 Powerful components, 10250 Simple parts, 335 Dextrous components, and 335 Precious components to craft them.

If Disassembling (T70-85):

28 weapon sets, 19 body armours, 18 leg armours and either -

65 augmentors, and 136 divine charges.

Or

2925 Base parts, 2925 Tensile parts, 2925 Flexible parts, 520 Enhancing components, 455 Powerful components, and 2720 Simple parts.

{How to get parts/components}

Base parts:
    Calculator
    Everything from the White Knight's shop
    Everything from the Varrock Sword shop
    Everything except battleaxes from the Warrior's guild
Tensile:
    Calculator
    Unstrung bows, Maple or better
Flexible:
    Calculator
    Unstrung bows, Maple or better
Enhancing:
    Calculator
    Ring of Slaying
    Empty Light Orb
    Lantern Lens
Powerful:
    Calculator
    Insulated Boots
    Polypore shop
    Spirit Terrorbird Pouches
    White Knight Staff, bought from shop linked above
Simple:
    Calculator, usually maple logs
Precious:
    Calculator
Dextrous:
    Calculator