Here are some quick and easy tips on how you can speed up and simplify your scanning with core probes. Please note this guide does not cover combat scanner probes which require different tactics sometimes.

This guide assumes you fly a ship with the usual scanning bonuses, like a scan frigate, T3 cruiser with CovOps subsystem or similar.
All of it still holds true for non-specialized scanning but you may need to decrease the scan radius in smaller steps.

Let's start!

• Always use 'Pinpoint formation'. Once set it will alway be chosen by default when you launch your probes. Spread formation is utterly useless for core probing purposes.
  
• First, do a full system scan. Depending on system size this can be from 16ly (small systems) to multiple 32ly scans (very big systems). The normal case is 16ly to cover most if not all sites. If there are only a few outside the scan radius it's better to chose 16 since this often saves you a whole scan on the covered sites. Then you can still do another 16ly to cover the remaining few.
  
• USE KEYBOARD SHORTCUTS to scan and change the radius. There are mousewheel actions which are slower and require more hand action. Try it out if you like, then go keyboard :D
  Bind: Scan, increase radius, decrease radius. That's it, the rest you do with your mouse.
  
• Doubleclicking on the system display switches between perfect topdown and perfect from-the-side view. This is IMPORTANT for the next step and much faster and precise than messing around freestyle click-and-dragging the mouse. A doubleclick is all you need (!)
  
• After the initial 16/32 ly scan, select a site to scan down.
  First, click once on the site to focus the camera. If you do not do this, the next steps might place your 'scan cube' slightly off the site.
  Now click and drag the cube side that is facing you. In topdown view it's the top side, in side view it's whatever side is facing you.
  Do this once in either topdown or side view until it aligns with the site. (the cube should be roughly on top of the red dot of the site)
  Then doubleclick switch to sideview.
  This time you do NOT use the cube side facing you but instead the big arrows extending from the cube, to position the cube on top of the site. Why? Because you already fixated 2 dimensions in the previous step. Using a cube side now would only risk to offset it again. Instead, use the arrows which only ever change the cube position in ONE dimension, which is the only one left.
  This is the power! This is the fastest and ONLY way you should ever, ever position your 'scan cube'. Freestyle moving with your mouse without using the topdown/side view approach is ridiculously slow and imprecise.
  Move down radius to 8ly if initial scan used a 32ly radius and down to 4ly if initial was 16ly.
  Remember to do the first alignment (in 2 dimensions) using the cube side facing you, then in the next step use the ARROWS to finalize its location.
  
• After you scanned the first scan with a 4/8ly radius its position will be more accurate.
  With a scan-bonus ship: decrease radius by 2 notches. Unless the site position changed drastically during your previous scan, in which case you may need to turn down only 1 notch.
  Without scan bonuses: decrease by 1 notch.
  Use your keyboard shortcut to do this. It's much faster than clicking in the UI and faster than using the ALT-mousewheel action. Particularly because ALT is a long way left of your mouse while you can bind all relevant keys to somewhere near your ENTER key.
  This may sound pedantic but it will save you many hours of lifetime during your Eve Online career. Keep the key bindings near your mouse so you can move and modify the scanning in a relaxed way without ever shifting your hands.
  I have bound increase and decrease to + and -, respectively, 'Scan' to the key directly between those. (EU keyboard)
  
• Repeat the cube move step (see 2 above) using topdown and side view and the clickdrag of the cube side facing you.
  The reason why you never use a different side is easy: The one facing you only moves the cube in the correct 2 dimensions for the view (one dimension is fixed which makes positioning so easy).
  
• With a 2-4 ly radius you should already see many sites for what they are and can decide if you want to continue or ignore that site.
  Wormholes in particular are usually discovered at 4ly radius, unless the site position jumped a lot in the previous step.
  If you continue, go down 1-2 notches (this comes with experience and differs by type of site) to get the final warp-to result.
  For example, wormholes usually get warp-to status after a 1ly radius scan while relic and data sites often require 0.5 to 0.25 ly radius because their signature is smaller.
  
• For the next site you want to scan, return to 8ly radius. Unless you didn't catch it in the initial scan, in which case you might need to 16/32 ly once more.
  
• Using Sisters of Eve probes over the regular ones gives you a small but noticeable bonus to scan strength. Their launcher and probes are not that expensive so if you scan a lot, be sure to use the Sister's variants.
  
• Last but not least, don't forget to collect your probes when you are done.

Give it a try and see how your scanning becomes so much more comfortable.

Good luck, capsuleer!