How do cyclists adjust their saddles to the correct height and fore or aft position?

The height, fore and aft adjustment for saddle is the same for all bicycles. You will find very clear instruction with photos from “Raleigh Bike Manuals & Quick Start Guide”.

From there, you can click on link to Raleigh bike Owners Manual. If the links I shared are broken, you can refer to the following question I answered earlier for other links and learn how to find your own bicycle owner's manual.

What are the best tips to maintain a bike in the proper way?

I extracted the following information from an older manual from Raleigh that I have:

“To adjust the saddle height, loosen the clamp bolt using an Allen key, spanner or the quick release lever and adjust the seat post to the required height. Adjust the height of the saddle so that when cycling along, your leg will be slightly bent with the pedal at its lowest point.

Important: When altering the height of the saddle, you must not pull the seat post out further than the limit mark (17). This must not be visible.”

Some clamps on seatposts are different but they are fitted to slide along the rails of the saddles in the same manner. These are the type of seat clamps that are often seen on alloy seatposts.

This is how the clamps with titanium bolts on a Prolite seatpost looks like.

This is how the saddle is attached to this lightweight seatpost from GUB. 

There are alloy and steel seatposts without clamps on them to attach to the saddles. Instead, the clamps are already attached under the saddles. As these clamps are heavier, you will not see them installed on road bikes. They are usually seen on saddles for cruisers or lower end bikes. For such, you loosen the nuts at both sides of the seat clamp to move the saddle forward or backward along the rails.

Cyclists of Canyon bikes, can even read about how they can adjust their saddle position and angle at the following link of their site. 

Bike Fitting for Road Bikes

If you prefer to see how the saddle height is adjusted, you can watch this video from Canyon Bikes.

The way the saddle from this Canyon Bike is attached to its seatpost is also different. You can see how the tilt is adjusted.