That’s a great resolution to have! I’m trying to be a bit more strict with my budgeting too.
Sorry if this sounds obvious or patronising (I don’t at all meant to!) and I’m sure you’ve heard this before, but I’d suggest starting with your monthly income, subtracting from that your main essential living costs (mortgage, bills, transport, phone, food, dental appts, clothes/school-related costs for your kids if you have any, pet expenses if you have pets) and seeing how much you have left.
Out of the amount you have left, you’ll probably want to allocate some of this for ‘fun stuff’ - e.g. meals out etc - and savings.
You could also consider giving yourself a monthly ‘budget’ in a different account to your normal one, if that helps with budgeting. For example, my salary gets paid into my main bank each month, but I have a separate account with Monzo, which is my ‘fun money’ for the month, which I put into different pots, as I find that a straightforward way of organising my money.
To help work out how much to save, perhaps work out how much you currently save and then work out if you want to increase that. I find it helpful to set up an automatic payment so the money I’ve allocated to savings leaves my account each payday and goes into my savings account, so I’m not tempted to spend it
Are you aiming to save for anything in particular? And out of the savings you already have, have you set aside some of them to draw on just in emergencies (e.g. house repairs, boiler repairs etc)? That’s always a good idea, as if you ever found yourself needing to draw on them, you wouldn’t need to get a high interest loan or anything like that.
Check every few months that your current savings and any money you’re adding to hour savings is in the highest interest account possible - perhaps lock some of it away for a few months or a year or two, as fixed rate savings will often give better returns.
And have you got any savings invested in stocks and shares? If you’re comfortable with the idea of stocks and shares and with not using that money for at least 5-10 years, I’d suggest considering investing some of your savings, as that can be a good way of getting good returns. Do make sure you have a good amount of cash savings (e.g. 3-6 months expenses) in an easily accessible account though.
Good luck!