The amount of pension you might need depends on a number of factors, including what your living expenses are likely to be in retirement and any other sources of income you might have.
For most they will need to cover their basic living costs, plus have enough to support any lifestyle expenses including travel and non-essential purchases.
For most people they will likely receive something from the States Pension and so subject to what they will receive, the amount they might need to save would be to supplement that amount.
The amount of pension you will receive depends on the type(s) of pension you have.
If for example you have made full contributions via social security during your working life, you should be eligible for the full States Pension.
If you have contributed (and potentially your employer) into any other type of pension you will also receive an income from that pension. The amount you will be paid from your pension will be dictated by how much you, and potentially your employer, have paid in and how the investments have performed.
In order to increase the value of your pension plan you can either pay into a pension for a longer period of time, or pay a higher amount in.
For anyone just starting out it is important to start as early as possible to maximise the saving time and potential for investment growth. It is also important to contribute as much as you can afford, as this can help increase your pension value long term.