I've seen some mentions of complete self surrender, or for example Krishna's 'abandon all dharmas and surrender unto me'. Fine, suppose I decide to do that. How would I know what God's will is at any moment? Whatever I innately feel like doing? I can never know what God's will actually is, only what I believe/feel it to be (which is probably wrong). Should I just forget all my duties and act spontaneously all the time? An adult can't function like that.
The will of god is not some esoteric unknown thing. It is mentioned in all vedas/dharma shastras/itihasa puranas.
Don't lie, don't steal, treat everyone with respect and love etc. - these are the common wills of god, applicable to everyone.
Study & teach vedas, fight for your country, do business, work under others - these are specific wills of god, based both on your birth and your qualities.
Do all of above without caring about results - this is the ultimate will of god, because it will lead you to moksha.
If you go to office and work, and you do it for money, you have to wait until end of month to get paycheck. But getting paycheck is not under your control, that is under company's control. If you get it, you're happy, if not, you're unhappy. That means, you voluntarily put your happiness in someone else's hands. But if you don't care about the money, and you're only doing it to help the company, that means you don't care about the results and you're happy as soon as you completed the work. The money may come, or it may not, but you don't care so you're carefree.
But how can anyone work without caring about money? What about food & mortgage & taking care of wife and kids ? Again, apply same logic. Just like you work to help the company, you use the money the company gives to help your family because it is your duty (which you decided to undertake when you got married). Forget about the fruits of helping your family, like a loving wife or obedient son because, those things are again like the paycheck, they're not under your control and may or may not happen. You'll be happy the moment you use the money you earned to provide livelihood for your family, and won't be worried about whether or not they will love you back.
This is what is meant in Gita - 'karmanyeva adhikaraste maphaleshu kadachana' - your rights are only to the work, not to the fruits.
Because you literally cannot control the results completely by yourself, you are dependent on others (not just other humans, but 5 elements, your body, god, all of them have to cooperate).
And as the proverb goes - 'atmavasham sukham, paravasham dukham' - independence is happiness, dependence is sadness. So the best way to be happy is to be independent, and the best way to be independent is to 'surrender' the results of your actions.
That doesn't mean you should do whatever you want (killing, stealing etc.) and not care about results. You should do what god wants you to do (dharma), and you should do it just because he wants you to (nishkamya karma - work without desire for fruits)
Think of it as your son obeying you just because you're his father, and for no other personal gain. Won't you be happy and shower him with love and give him whatever he needs ? That's what god will do if you obey him just for sake of obeying. But you don't even care if god does you any good in return, because you can derive happiness simply by following his orders. And finally, when you get bored of even that happiness, then there is nothing holding you on earth and you attain moksha and you are always happy.