There are some interesting replies on the thread. I think what you must ask is how you wish to answer the question? If we are talking purely on a personal perception level then most of the replies give an answer of what the average lay-person understands "class" to be.
If we are talking about technical understandings of class then it is probably best to look towards Sociological work and studies carried out on social mobility.
What you tend to find when looking at these studies is that money and jobs can lead to prestige but the Sociologists will also use other yardsticks in which to judge a persons class. Of course this class is not just split into working, middle and upper.
As stated above Sociologists do not just assess income as a form of mobility as it can only be considered as only one dimension to class. J. H. Goldthorpe (1935) devised a schema to divide and show difference in class. It is divided into seven categories which are listed below:
Higher professionals, higher grade administrators, managers in large industrial concerns and large proprietors.
Lower professionals, higher grade technicians, lower grade administrators, managers in small businesses and supervisors of non-manual employees.
Routine non-manual, mainly clerical and sales personnel.
Small proprietors and self-employed artisans.
Lower grade technicians and supervisors of manual workers.
Skilled manual workers.
Semi - skilled and unskilled manual workers.
Using this system studies have attempted to show the shift in peoples standing within the class system. What you will tend to find is that people largely stay within the class in which they were born. They may move within a few categories which is known as short range mobility. There are of course people who make large jumps within the system and this is known as long-range mobility.
More importantly there is mobility between generations i.e. father and son. This is known as Intergenerational mobility and the area most studied by Sociologists.
What does this show though? In simple terms some studies show we have mobility and therefore can "change our class". However the mobility observed tends to be short-range and very little movement occurs between class 7 and 1 for instance.
Of course there are many studies and for every study that supports the Functionalist view of mobility based on merit there are equally as many if not more Marxist studies showing little mobility with the real power restricted to those at the top and not offered to anyone else.
If I was to give an honest answer of what it means to be working class I could not give it, hence my ramblings above! I believe the lines nowadays are so blurred it is difficult to pass judgment hence the different yardsticks used by Sociologists to define classes. Once study goes as far as to ask the sample how many holidays they have a year and do they have colour T.V !
You could have someone who earns good money and lives a 'clean life" and still classed as working class by you, I, or even a Sociologist. Whilst a person in the same street on benefits and no desire to participate in society etc deemed working class also.
I guess the burning question is not how do we assess it, or even what constitutes it but rather, does it matter in the modern world?
I would suggest that in the majority of everyday occurrences and instances it does not. However and it is a very big however, it CAN matter and tends to be where positions of power within society occur.