If you have any debts, then it is usually cheaper to pay them off than save money. This will depend on the type of debt and how expensive it is, but you should take a look and find out. Debt is usually more expensive than any interest gained by savings and therefore taking a small chunk off your debts each month instead of saving money will make a significant difference to you financially.
Assuming that you have no debt, then you need to address the issue of how much to put in a savings account. It is worth starting by calculating how much you usually spend and how much you get in income each month. This may not be the same each month, but an average will be good enough at this stage. You will get an idea of whether you spend more than you earn, you spend everything you earn or you tend to have some left. If you have money left each month, then it is easy to see that you should save that much each month.
It is wise to set up a direct debit to put money in a savings account each month when you get paid. This means that it will be harder for you to spend it. If you wait until the end of the month and transfer out whatever is left, you will not budget so well as you will have that money to fall back on.
If you generally spend more than you earn or break even then there is nothing to save. If you wan to have extra to save or at least not be getting into debt each month, then you will need to make some changes. You will either need to earn more, spend less or both.
This is not as easy as it sounds of course, but once you know that you need to address it, then at least you can make a start. Earning more will usually mean finding a better paid job, working more hours, asking for a pay rise or finding a second job. Spending less will need research into where you can purchase things more cheaply. It may also require you to cut back so that you are buying less things as well. It can be quite a change to make, but if you are determined to save you will need to have a go. There may be just a few change that you can make and then you will have some extra money each month that you will be able to save.
So how much you save very much depends on your own personal circumstances. It has been said that it is wise to build up a pot that will cover you if you are out of work for six months, just in case you get made redundant. However, it is wise to consider other things that may happen in the future such as retirement or illness where you may need to fall back on your savings too. There would certainly be no harm in having more than you need.