Do you have a CV/Resume, artist statement, bio, images/portfolio with descriptions ready to go? This is a working portfolio that you should always be updating.
Can you explain or describe your work and what you do within 1 minute or less? Practice this with friends. Videotape yourself and watch, use your artist statement to help you, and always refer to work you have made.
Does this opportunity fit within your scope of what you need now as an artist, for the future? Some residencies and grants are suited to more experienced artists or artists of specific mediums, ethnicities, genders, etc. Please read the fine print and look at who has been there.
Does the application cost money, and if so, are you willing to pay? Try not to spend too much money unless you really want to be there. Some applications cost money, some residencies cost money, others do not.
Do you have a smart portfolio of images and work that is well documented? This is hyper important for success. Format images to same size and only show images that are clearly readable. Always put your best work and the work your most proud of first. Sometimes various juries only look at the first image or so.
Do you have at least three references that would write on your behalf that know you and/or your work? Ask them before you write them down. All letters take time, so plan ahead. Remember these people are doing you a favor.
What artists, colleagues, peers, do you admire, and where have they been?
Have someone look over your application, portfolio, and writing before you send it off to make sure that everything looks good and makes sense. Reading your writing aloud can often times help you find the areas of work that need to be edited. Get help here, go to a writing center and show it to your friends for their opinion.
Can you take multiple rejections before you are awarded a residency, grant, internship, or job? Many people apply upwards of 25 or 50 times before being accepted into a program. Please remember, never give up!
Plan ahead, many applications are sent out up to two years in advance.