If you aren't already in a relationship, start out remembering that this is an important issue to a relationship's survival. Keep in mind that how a person spends on a date does not necessarily reflect their attitude toward budgeting, either. Many tightwads spend money on a date that they will later be uncomfortable spending in a relationship, which is an unintentional form of false advertising. You need to actually talk about money before you go from dating to relationship (I find it amazing that people can talk about and have sex but are too embarassed to bring up money).
If both people are tightwads, then they're probably well matched as long as they can work out the details. If both people are spendthrifts, well, they're probably well matched again, though I suspect they'll have a rude awakening to reality eventually. But if one is a tightwad and the other is a spendthrift, they really need to work out how finances will be handled before beginning to share expenses.
You need to find a way that works for you, but keep in mind that if one partner is a spendthrift and goes along merrily knowing that the thrifty partner will bail him or her out, you have a recipe for a LOT of conflict. The same goes if the thrifty partner tightly controls the money and the spendthrift feels angry or poor. If neither partner is willing to compromise, then you may need to think long and hard about whether you really want to be in this relationship. Even if you just live together, getting back out of a relationship is generally expensive.
I rather like my daughter and her partner's solution and variations on it. They calculated monthly expenses, plus a bit extra to go into their emergency fund, then each put half that amount into a checking account that my daughter uses to cover the bills and manage their emergency money. I think some bills they are individually responsible for as well. Then, whatever is left, they each can spend or save as they like. Her partner has the option to blow all of his extra on toys (which he does not, btw), and she has the option to squirrel away hers, and both feel they have control of their money.
It seems to be working well for them, though she's pointed out that talking about things and respecting the other's feelings is VERY important. And they're learning from each other. Many of his expenditures are for practical things that they can both enjoy for a long period and she has been able to admire many of these choices, and he's seeing the value of having emergency money and little or no debt.
A variation on this that works for some families is to divide the bills, with each partner responsible for certain bills. My recommendation here is that the more responsible partner be responsible for the most vital bills, such as the mortgage or rent.
One that I personally don't like but seems to work for some couples is for one person to be solely responsible for all the money and bills, with the other asking for cash or getting an allowance as needed. I know one couple that this works very well for, but they have an unusually strong, trusting relationship, and the person managing the money is very sensitive to the other partner. They communicate about things a lot. For a couple that can communicate this well, this can work very well as a solution when one partner is a spendthrift but wants to do better. Far too often, however, I've seen this approach lead to just as much or more conflict, and sometimes outright abuse as the person with the pursestrings uses it to control the other person.
The important thing is to find what works for you. And even if you think you're being cautious, you may find that the person changes later. When I met my ex, he had a nice bit of savings and seemed to be reasonably frugal while also willing to spend a little on fun. I never talked specifics to him about budgets, though, then after we were married discovered he had very different ideas. Later, he wore me down about credit cards, and although he'd promised we'd pay them off every month, he immediately began maxing them out. My mistakes were not talking to him about details of handling money and priorities, and, frankly, what he wanted out of life. I'm still not sure he knows the answer to that last question...