The UAAPDA hosts grant writing workshops on campus througout the year to meet the demands of the current cohort of fellows. These are typically hosted by Faculty with wide and extensive experience securing funds from NIH, NSF or other smaller granting agencies.
There are many resources available online:
Nature hosted their first Webinar: Writing a successful grant proposal in September 2015. Acess to the podcast and slides is still availble through this link (here) and simply requires you enter your name and email and click 'register'.
Many blogs offer general tips and advice.
The NIH has generated a podcast series which includes advice for early career scientists.
UAA Office of Grants and Contracts also provides grant assistance, and has collated a series of grant-writing tips (see pdf below).