The standard approach to budgeting is to break your expenses down into categories, like “Rent,” “Groceries,” “Travel,” and so on, and give yourself a certain amount of money every month to spend on each of those categories. This is a good way to ensure that you don't overspend on any particular category.
To make this process really tangible, some personal finance experts advocate the “envelope method:” get a handful of envelopes, label each one with a spending category, and on the first of the month fill each envelope with the right amount of cash. When the “Dining Out” envelope is empty, it's time to cook.
This approach might work great for you! It has a few downsides, though: for example, you can't use credit cards, which can save you a lot of money with rewards. It also involves lugging around a fair amount of cash (or planning ahead).
There are some great online budgeting tools out there—You Need A Budget (“YNAB”) is an especially popular choice.
Personally, I don't budget this way. My expenses (especially for travel) tend to vary a lot from month to month, so my estimates for some categories are often drastically wrong. Also, to be honest, I'm lazy! Rigorous budgeting is hard work.
My approach is a little different. Since my primary goal is to maximize my savings rate, I start out by deciding how much I want to save each month. I've configured Vanguard to automatically pull money from my checking account every month, contributing to my IRA and a taxable brokerage account. Anything left over in the checking account is, as far as I'm concerned, a big ol' slush fund. I don't bother budgeting by categories.
Let's phrase this another way: I've got a single category in my budget labeled “Expenses,” and the balance of my paycheck is invested. I find this to be a lot simpler, and it still ensures that I'm meeting my savings goals.
A third way to phrase this idea of reverse budgeting is captured by the old financial advice to “pay yourself first.” Before you pay your other expenses, be sure that you're paying your future self by investing a certain amount.
That said, I do still track my purchases (I've recently stopped resisting and started using Mint, which does the job well), and I regularly check in to see how much I'm spending on each category. Having a general idea of how much you tend to spend on housing, food, and so on is still useful.