It really depends on the field. Many grad schools want to see some professional experience in their applicants. You can successfully apply to law school or med school straight out of undergrad but it’s almost unheard of to get into a highly ranked business school without a few years of experience. Public Health, Education, Public Policy and many other fields are somewhere in between.
In any case get as much exposure to the field as possible by participating in internships, research, volunteer, summer jobs or other work. Not only will they help beef up your resume but they’ll help you home in on what you want to do and why.
Get to know your professors. The more they know and like you the better the possibility they’ll write you a positive recommendation. Depending on the field (for instance academic fields like mathematics or history) and who the rec. is from this can be one of the most important elements of your application. When I worked in a doctoral program at an Ivy League U. many moons ago and sat in on the admissions committee I would sometimes hear people say things like “Joe Professor at Peer University says this kid’s really bright. I gave him a call and he convinced me to take a chance on her.”