There is a book called "How to Watch Motor Racing" by Stirling Moss, (it's available second hand from Amazon) and although it is terribly out of date now, it is a jolly good read. In it are (amongst other things) instructions about how to keep a lap chart. In essence, all you do is to write down the numbers of the cars each time they pass you. Write them down in a column, starting a new column each time the leader comes past. Here is a photograph from the relevant page in Stirling's book - you can see how number 7, having led the race until just after half-distance, drops out, and number 17, starting from the back, comes through to finish on the podium.
This chart is very useful, and relatively easy to produce for short races. It helps if you can write quickly, legibly, and in a straight column, without having to look down at what you're writing.
Note though, that when the leader starts to lap the backmarkers, you have to record the backmarker in a previous column - he has not, after all, completed the same number of laps as the race leader. This is where it gets difficult with a long-distance race: the leaders will lap slower cars many times and even the mid-field runners will lap those at the back. Here is my block lapchart for the 1000km race at Brands Hatch in 1986.
Things to note (you might have to expand the photo):
The trouble with trying to keep a block chart going is that you will often get three cars crossing the line close together, all on different laps, and by the time you have found where they all belong on the chart, another two cars will come past and you easily get lost.
The answer is to have an assistant, doing a "running chart". This merely records the number of each car as it comes past, in the order that the cars are running on the track. Don't worry about which cars are a lap behind, just make sure that you record each car. Start a new column every time the leader comes past, just because it is a good check on how many laps are completed. In the early stages, of course, before the lappery starts, it will closely resemble the block chart, but as the race develops, it provides the raw data input required to facilitate the block chart. Indeed, the first time I enlisted a helper to do this, I ended up spending more time looking at the running chart than I did looking at the cars on the track.
If you looked up TSL's website before (to look at a position chart) - look now for what they call a "Lap Chart", and look at the column containing the car number. This gives the order that the cars cut the timing beam, and effectively shows what the running chart looks like. Of course some columns are longer than others, depending who rejoins from pit stops, or whether the leader has stopped.
So to summarise (for the benefit of Chris, who asked the question) a block chart shows you at a glance the position of each car, and how many laps they have all completed; whereas the running chart just shows the order that cars are running on the track.
If you're quick, and have a stop watch, you can make notes on the running chart of the gaps between significant cars - this way you'll pick up who might be closing on whom, and whether a pass for position might be on the cards. Even with electronic timing, I still find a lap chart massively helpful, not only in following a race as it unfolds, but also to keep as a record of what happened.