This post asks for resources to handle the following situation: "I, suddenly, have students" and many wonderful answers have been provided. My question here is sort of a prequel: recently, a post-qualification second year graduate student $X$ expressed an interest in working with me.
What should I put $X$ through before agreeing to advise him or her?
I don't mean to ask about the part where I point $X$ to appropriate literature from my field and help $X$ to understand the textbooks and survey papers as needed: that I can do. But how should I measure $X$'s aptitude and gauge interest levels, etc? I don't want this to be a long and drawn out process for obvious reasons. The zoomed-out version of my question probably should be:
What do you look for in a graduate student before you agree to advise him or her?
If it turns out from the responses that this question is overly subjective and leads to wildly varying opinions, I can make the question community wiki.