I've tackled emergency funds, paying annual bills, and saving up for large purchases, and this time am going to begin the subject of saving for retirement. (Remember - I am not an expert, so deal in these questions in fairly broad terms...)
In summary, while most of us working now may receive some kind of state pension on retirement, it seems likely that the vast majority of the money we need to live on in retirement will have to come from our own resources.
There are various possible sources for this income, the most obvious and generally applicable being a pension, to which we will have contributed while working.
There are essentially two kinds of pension; one, a 'final salary' pension which is based on receiving a proportion of the salary you are earning just before retirement, for the rest of your life, and often involves a lump sum being paid on retirement as well. The proportion of your salary which you will receive will depend on how many years you have been a member of the scheme. Final salary schemes are currently available to those working in the public sector, as well as in a very small, and declining, number of large corporations. The advantages are obvious, and the contribution you will have to pay as an employee relatively small compared to the benefit of a decent, guaranteed income in retirement. It may be worth making additional contributions in order to get the maximum benefit from these schemes, if you join late and can afford to do so.
The second type of pension is a 'money purchase' scheme. Under this scheme, employee and employer will usually each contribute a percentage of the employee's salary into a pension fund, which will build up into a sum that can be used to buy an income for the rest of the employee's life when he or she retires. Usually the pension will be held with a financial institution chosen by the employer, but the employee will often have a choice about which funds they invest in, and which are most appropriate will depend on your age, and how much risk you are prepared to take.
The pension contribution offered by different companies will vary, and companies generally match the employee's contribution up to a certain maximum, normally around 5%, maybe up to 10% if you are lucky. It is worthwhile thinking about making the maximum contributions in order to get the greatest benefit from the employer contributions, if you can afford to do so. On retirement, the money in your fund, which will hopefully have grown considerably over the years, will be used to buy an income for the rest of your life, called an annuity. There are various factors which will influence the value of your money purchase pension, including how much you have managed to contribute, which funds your money has been invested in, how much these have grown, and annuity rates - the rate at which it is possible to buy an income - at the time you retire.