Please note that we are assuming that you have a choice in this matter: The primary difference with not having a choice is that fixed expenses are either higher or pretty much equal to income with people who are forced to live on a budget.
Frequency of refreshing the budget
Weekly seems the preferred timetable: It allows for clear fixed day cutoff, whilst not being as inflexible as daily, you will not be able to do any spending with a tight daily budget; weekly allows some room for a bit of discretionary spending. Monthly is also possible, but if you get a monthly income there is a risk of big monthly splurge where you buy everything you want and are broke the rest of the month. Besides, all weeks are the same length, where months differ up to three days.
If you have some money left at end of the week: Keep it in your budget, whilst still adding to full amount for the new week, this creates the possibility to save for something without tapping into your actual saving.
Fixed expenses
These should be separated from your budget, as you are not able to choose freely when or how to spend this. Using two bank accounts usually helps, but simply writing it down somewhere, possibly just how much you spend on these each month, will do fine.
It is important that you do not blindly add to these, because they are not budget relevant, to be able to afford more. In the long run, fixed expenses are the key to having savings so should also be minimised.
Keeping your fixed expenses account also as your general savings account is fine, as long as you have no problem remembering how much is needed and when it is needed.
Groceries
Everybody has to eat and drink (water, not something alcoholic), therefor we will consider these expenses to be mostly fixed. There is a difference between discretionary and non-discretionary spending here: Basic food, such as bread and vegetables, are to be considered fully fixed, as you need them to stay alive. Candy and tasty beverages are not fixed, they are luxury spending and should as such be expensed from the non-fixed budget.
It can be difficult to pay for groceries from two separate accounts, so it is possible to look over your receipt afterwards and transfer amounts from one account to the other.
Relations
Humans are social animals, but they can lack understanding for the situation of their peers, even close friends. It has happened to the author several times (both privately and professionally) that he was forced, as close to as legally possible, to spend money on things for which he did not have the budget. These expenses can be either an assault* on you budget, or they can cost you a good relation with your family/friends. This is a choice you need to make for yourself, but if you can spare the expense, it might be a lot easier to simply go along with it.
Hobbies
We all have things that we like to do for fun, and unfortunately for us, most of these things cost money. Most hobbies have a fixed and variable cost component, which we will have to split for budgeting purpose: The fixed part includes not only membership fees but all regularly recurring cost, such as maintenance and depreciation of gear (provided that not replacing or maintaining will result in not being able to do the hobby). There also are variable costs, such as new or fancier widgets that you do not really need but really want. Social outings could be considered as variable, depending on their degree of required.
A unpopular argument follows: Most hobbies are just ways to fight of boredom, so replacing it with something more productive is an option. If you replace it with something that brings in money or can go on with indefinitely, you will actually be saving some money. In this point of view, the entire hobby is fully variable.
*It is not inconceivable that a manager will use you not going with the crowd against you, that genuinely happened to the author.
