Connect with the advisor you want to work with before applying
Showing interest and/or knowledge in their past and current research is a plus
One option is to go to their lab's website and look at the research completed and in progress there
Or type their name into google scholar and read the abstracts of the papers that come up there. You could also try emailing to ask which papers represent their research interests (note: professors are busy so prospective student emails are likely to be last priority)
Ask the professor what they look for in a graduate student (GPA, experience, skills, level of creativity etc.)
Research experience is always a ➕
Professors/Advisors usually are looking for students who demonstrate ability and experience creating a research question, setting up an experiment, and getting creative enough to answer that question. Ways you can demonstrate this are through:
REUs: Research Experience for Undergraduates are like internships but more research focused. I would argue that REU > Internship for students heading in the grad school direction but it is definitely debatable
Internships: Explain your role in whatever part you played on your project. Even if you don't think it was very significant (although I'm sure it was) you never know if that advisor is looking for that specific skill
Undergraduate Research Assistantships: I went about this by just finding a professor on campus whose research I liked, and asking them if they had room for an undergrad. Even if it was just performing a literature review, the experience was still valuable. You can also find out about the research at your school by going to your university's Undergraduate Research Office (DO THIS!!!!)
Explain any discrepancies in your application (This also applies to fellowship applications)
*Decent* reviewers should understand that certain aspects of your application package (GPA, Experience, GRE etc.) can fall short for reasons out of your control. I feel like it's better to explain these discrepancies in your personal statement than to surprise them. It doesn't hurt to explain if there were any external circumstances (in accordance with your comfort level) that led to less-than-stellar performance.
DISCLAIMER: You will have to use your best judgement here with what you decide to share. I have heard of some instances where this hurt the applicant. I can only speak from my experience where a reviewer noted my explanation was helpful in their feedback.
Just apply :)
Sometimes this is the hardest part. The worst they could say is no.
These are the tips that are fresh on my head right now. If I have anymore, I'll add them to this forum post by using the comment area! If anyone has experience and any advice to share, please feel free to do so below!