Repasting laptops

Laptops are very picky about the paste used. due to the small dies and the concentrated heat, pump-out is a real phenomenon that makes temperatures degrade quickly. For this reason, high viscosity pastes like IC diamond are recommended.

Pump-out: Hot things expand, cold things contract. Apply this knowledge to the components and you get expansion and contraction of the metal surface between the component and the coldplate (the copper plate on the heatsink that transfers heat from the component to the heatsink). Due to these expansion and contraction cycles, it can create air pockets in the paste or push paste out, resulting in pump-out and worse thermal performance.

What to buy?

The best non-conductive thermal pastes available are:

IC Diamond. Best For Longevity. It's an excellent paste, but it is slightly abrasive. If you're planning to remove this paste in the future, make sure to use soak the paste using isopropyl alcohol, wait a minute, and then gently remove it. Keep doing this until it's fully removed. If the paste leaves a stain on the copper, don't worry about it.
Note: "karat" simply denotes the size of the tube, and is irrelevant to its performance.
Gelid GC Extreme. Very good paste, on par with ICD, but does not last as long (both the tub and the application). Buy smaller amounts if you will not use it often and buy new tubs in a year or two. It isn't as versatile as ICD so if your heatsink is bad, you may need that instead.
Coolermaster Mastergel Maker/Nano.
Phobya nanogrease extreme.
Thermal Grizzly Kryonaut requires a FLAT heatsink. Socketed CPU and MSI laptops usually qualify, most laptops will not make good use of it. Do not buy unless you are willing to use it as a trial and error paste, or you know your heatsink is very flat (like if you own a MSI GT75 or something).
This paste may dry out above 80c degrees. this is stated on the product own's page
Arctic silver 5. Last resort

Arctic Céramiqué 2. Special mention. This paste is nowhere near as good as the above, but it is two things: cheap, and a great filler paste like ICD. A tube of 25 grams (imagine doing about a hundred applications) is roughly $8 on amazon in the USA, and a similar price in various other countries. If you have a low powered laptop and just want something decent and cheap, this is it. If you want to practice doing repasting, this is your go-to. If you want the best performance, look above instead.

Some thermal pastes you should avoid: nutella, mayonnaise, tooth paste, NT-H1, KPx, MX-4 (they are not good for laptops) and ANYTHING ELECTRICALLY CONDUCTIVE.

Procedure

Remove the heatsink using the correct sized screwdriver, DO NOT STRIP THE BOLTS AT ALL COSTS.
Clean the paste off with isopropyl alcohol, ideally with a coffee filter
Let it air dry
Apply the paste on the processor, usually in a line. Keep in mind that you can't really use too much paste as long as the paste is not electrically conductive (most aren't). It is better to use slightly too much than too little.
for the GPU, apply dot method or cross depending on die size.
Reassemble the cooler with sufficient pressure. The screws should be screwed in with a star/cross pattern to keep even pressure on all sides while tightening. Do not overtighten, but make it snug.