Before we start, do have a read of this page which is ostensibly about mooring costs but in which I inevitably had to describe various types of mooring so there’s a lot of crossover with what’s written below.
In terms of mooring, you are generally permitted to stop anywhere on the towpath side of the canals, provided that there are no official signs to indicate otherwise and as long as you are not causing an obstruction (such as mooring in a winding hole, on a water point, too close to a bridge hole etc).
You’ll (sadly) be amazed at how many boats think it acceptable to moor in stupid places that block access for someone else, such as on lock landings or on the water points. Often they are novices who simply haven’t realised the folly of their ways and a gentle bit of instruction will see them moving but sometimes they’re just aggressive selfish folk who couldn’t give a toss and will let you know in no uncertain terms. Thankfully this is rare.
General towpath mooring on the canals comes with a 14-day limit unless otherwise marked. Yes, the CRT do check – they have towpath rangers who potter along the canals noting down boat index numbers and the dates they were spotted; spend too long in one spot an you’ll find a note left on your boat advising you to move on. Failure to do so eventually ends up with court proceedings against you but that’s a very protracted process.
The canals also tend to have some spots specifically marked as “visitor moorings’. These will be in popular locations such as some towns or beauty spots. They will often have a limited time such as 7 days, 48 hours or even 24 hours in some cases. The idea is to ensure boats don’t overstay and hog the best locations so that everyone gets a fair chance of stopping at the best spots.
River mooring is a very different matter as the land on either side is often privately-owned rather than under the control of the navigation authority. You will therefore only be permitted to tie up by permission of the land-owner. On rivers such as the Soar and the Trent, there are official overnight visitor moorings at some locks (yes, this sounds as though it contradicts what I just said about mooring on lock landings, but these are specific, marked mooring spots adjacent to the lock landing that you’d use when going through the lock. It’s very obvious when you see it, fear not).
On rivers such as the Thames, there are plenty of places to stop but they usually come with a fee payable for each night, and stiff penalties for overstaying. These would be enforced like parking overstays with a car, through a civil court procedure.
On the canals you will often find that you can’t get the boat tight into the side due to build-up of silt. This can be rather frustrating but it’s usually worth just going on a little further and seeing if it was just a localised issue. Sometimes just moving 100 yards or so will sort the problem.
On the Shropshire Union canal (the ‘Shroppie’) the situation is more extreme in that large sections of the canal are lined by an underwater concrete shelf which you can’t see but will feel as soon as you try to come into the side, scraping your boat on the concrete. It makes tying up to the side incredibly frustrating and experienced boaters will often carry small ‘go kart’ tyres which they float on their side between the boat and the canal-side, so as to keep the boat pushed away from the shelf. You have been warned!
I repeat, it’s advisable to also read the page I wrote about mooring costs in conjunction with this one, to get the full picture.
 Almost always it is only the towpath side that is permitted for mooring; the other side tends to be private land and is generally less accessible anyway. Don’t moor here unless you know it’s permitted eg by official signs.