Intro
These glowing slugs are found all over the map in different places and they can be either blue, yellow or purple. When you collect your first slug ADA tells you to research it in the MAM however the Power Slugs research branch won't appear in the MAM until you collect a blue one, until then the research branch will be called Strange Energy Readings.
Power Shard
Once you collect the first Blue Power Slug you'll unlock the more research branches and you'll now be able to craft a Power Shard at the Craft Bench or in a Constructor. 1 x Blue Power Slug can be turned into 1 x Power Shard.
Overclock & Underclock Production
The Power Shard will have no purpose until you research Overclock Production which requires 1 x Power Shard, 25 x Iron Plate and 50 x Wire. Once researched you will now be able to adjust the speed over machines using overclocking or underclocking with Power Shards. By default a machine runs at 100% clock speed.
If you overclock a machine to 200%, you'll need twice the amount of input items and it will produce twice the output at twice the speed, with the drawback of using significantly more power.
If you underclock a machine to 50%, you'll need half the amount of input items and it will produce half the output at half the speed, with the upside of using significantly less power.
Machines accept up to three Power Shards, each Power Shard can allow the machine to be overclocked by up to 50%, so thats 150%, 200% and 250%. You can overclock to any number you like as long as you have the correct amount of power shards, for example 137%.
As for underclocking, no power shards are required, the only requirement is to unlock the research in the MAM.
So why would you overclock or underclock a machine? You might have built a factory and you did not put the correct amount of machines down, so instead of rebuilding you could overclock the existing machines and provide the correct amount of resources. Or perhaps you need 1.25 machines worth of something for another machine, overclocking the machine to 125% would mean you only need one machine.
Same logic applies to underclocking, your recipe may only require 0.4 of a machine, if you leave it at 100% it will saturate the output and eventually stall which will make your machines run inefficiently and also start / stop a lot more. So underclocking that machine to 40% would make everything run efficiently.
Power generators are another example of where overclocking can be useful, for example with power generators if you overclock them to 250% and feed them with the correct resources then you're simply building less generators for the same amount of power. Of course you'll need to collect those power slugs to be able to turn them into Power Shards, or automate them later in the game.
There's no right or wrong way, it's just another option to help you with your factories.
Slug Scanning
Slug Scanning is another research Branch that requires 50 x Iron Rod, 100 x Wire and 200 x Screws and will provide the ability to locate Power Slugs using the Object Scanner.
Yellow Power Slug
The middle research branch will first allow you to turn Yellow Power Slugs into Power Shards, requiring 1 x Yellow Power Slug, 25 x Rotors and 100 x Cable. 1 x Yellow Power Slug can be turned into 2 x Power Shards.
Purple Power Slug
Next you can research Purple Power Slugs which requires 1 x Purple Power Slug, 25 x Modular Frames and 100 x Copper Sheets. 1 x Purple Power Slug can be turned into 5 x Power Shards.
Synthetic Power Shards
Finally the last research for Power Slugs is the Synthetic Power Shards, this requires 10 x Power Shards, 100 x Time Crystal and 200 x Quartz Crystal. Once unlocked you'll be able to automate Power Shard production in the Quantum Encoder, which is required for the Alien Power Matrix and Ionized Fuel recipes.
With all the research done you'll have completed this branch of the MAM. Here's a tip you might find useful, night time is a great way to search for Power Slugs as they are very easy to spot.