Depending on the area, a graduate program may receive anywhere from 50 to 500 applications in any given year. Most of these applicants are going to have high GRE scores and good grades or they wouldn't be applying to graduate school. All of these applications are going to be thrown into the pile. The longer you stay in the pile, the better your chances are of getting into the school. If you have the basic credentials, the things that enable you to stick out from the rest of the applicants are going to get you admitted into the program.
Most graduate programs are at large universities where faculty are under pressure to publish.
These are skills faculty members won't have to spend time teaching a new student. There are a number of ways. You can begin by looking up your undergraduate professors' names in the literature and seeing what types of things they are interested in, asking other students around the department, or simply going up to your professor and asking. Ask the faculty at your undergraduate institution for help on a research idea you have developed. If you don't have an idea, even a rough one, ask to help your professor with entering data, searching the library for relevant literature, or collecting the data on one of their projects.