As one of my favorite happiness and work-life balance researchers likes to say, "Develop good habits; you won't need as much willpower that way." With anything new and difficult (like starting the process of becoming a competitive fellowship applicant), I need to start with the smallest step and practice every single day. When it's a tiny action, it's less intimidating to get done but once I've developed the habit, I get on a roll.
Where are you in the process of funding your dreams? Are you still in the dreaming phase? Have you figured out the perfect fellowship to apply for but haven't gotten down to writing the essays? Wherever you are, just start doing a little bit of the work every day. You'll find that instead of dreading the task of getting back to work on the application, you'll look forward to it. Where previously you may have had to spend half an hour reviewing where you left off (months ago) before you actually get meaningful work done, now you'll start fresh and current each time you get to work. Your mind will start brainstorming before you even sit down to work and you won't have writers block.
For me, the best way to make progress is by taking tiny bites each day and committing myself to work consistently (even if its just gradually).