The System helps those who know The System. A successful grant proposal submitted by someone else to a specific grantmaker is a good example - analyze what made it successful. Know the funding limits, stated or implied, of the grantor when designing your budget request. Use the telephone to get to know granting officers and solicit their expert advice. Know your colleagues, and ask them for help.
Research is highly interdisciplinary and no one person can do it all.
Colleagues are essential for ideas, critical review, teaching you techniques you don't know, and suggesting funding sources. Colleagues often have experience reviewing grants and may know the work of people who will review your grant. As you mature in your discipline, cultivate relationships with younger scientists with fresh ideas and new techniques. Know what you do well and have examples of data and publications to prove it. Know what you cannot do and seek collaboration.