I started storing and summing all my receipts, bills, etc. It has the advantage of letting me separate expenses by category, but it's messy and it takes a long time.
It sounds from this like you are making your summaries far too detailed. Don't.
Instead, start by painting with broad strokes. For example, if you spent $65.17 at the grocery store, don't bother splitting that amount into categories like toiletries, hygiene products, food, and snacks: just categorize it as "grocery spending" and move on to the next line on your account statement. Similarly, unless your finances are heavily reliant on cash, don't worry about categorizing each cash expense; rather, just categorize the withdrawal of cash as miscellaneous and don't spend time trying to figure out exactly where the money went after that. Because honestly, you probably spent it on something other than savings.
Because really, when you are just starting out getting a handle on your spending, you don't need all the nitty-gritty details. What you need, rather, is an idea of where your money is going. Figure out half a dozen or so categories which make sense for you to categorize your spending into (you probably have some idea of where your money is going). These could be loans, cost of living (mortgage/rent, utilities, housing, home insurance, ...), groceries, transportation (car payments, fuel, vehicle taxes, ...), savings, and so on -- whatever fits your situation. Add a miscellaneous category for anything that doesn't neatly fit into one of the categories you thought of. Go back something like 3-4 months among your account statements, do a quick categorization for each line on your account statements into one of these categories, and then sum them up per category and per month. Calculate the monthly average for each category. That's your starting point: the budget you've been living by (intentionally or not).
After that, you can decide how you want to allocate the money, and perhaps dig a bit more deeply into some specific category. Turns out you are spending a lot of money on transportation which you didn't expect? Look more closely at those line items and see if there's something you can cut. Are you spending more money at the grocery store than you thought? Then look more closely at that. And so on.
Once you know where you are and where you want to be (such as for example bumping the savings category by $200 per month), you can adjust your budget to take you closer to your goals. Chances are you won't realistically be able to do an about-face turn on the spot, but you can try to reduce some discretionary category by, say, 10% each month, and transfer that into savings instead. That way, in 6-7 months, you have cut that category in half.