This is one of the contenders for Best Question Ever, and, of course, there are entire books written on the subject.
But there's reading or hearing about a subject, then there039;s "knowing" it.
So. Putting aside the obvious (great real estate agent, mortgage broker, home inspector), what's of supreme importance is that YOU start with a very clear picture of WHAT YOU'RE LOOKING FOR IN A HOME!
You have to prioritize. Some things are inflexible - you can't afford more than you can afford, for example. Other things are so offensive that they'd make it not worth buying a home - for some people, it's lack of an ensuite master bath, or a formal dining room, or too much or too little garden space, or too much traffic noise . . . it's good to ask the question, "would I go into debt to live here?!"
You have to be a good communicator. You have to be assertive and clear in your statements, and ask questions until you get a satisfactory answer. And you should be willing to accept, "I don't know, but I will find out," as a satisfactory answer - so long as they find out!
And, it helps if you're a good listener.