The first and most obvious thing to do is to read the advice offered by your funding agency. In the case of EPSRC, the primary funding body for computing science research, there is a "Guide to EPSRC Research Grants". We make no attempt to duplicate the material in the EPSRC guide or any other; you must get yourself a copy and follow the guidance closely.
The most substantial part of any grant application is some form of "Case for Support". It is this case which will persuade, or fail to persuade, your funding body of the value of your proposal. Proposals range very widely indeed in their quality. You can improve your chances enormously simply by ruthlessly writing and rewriting. This document is entirely about improving your case for support.
There are two vital facts to bear in mind:
* Your case for support will, with luck, be read by one or two experts in your field. But the programme manager, and most members of the panel that judges your proposal against others, won't be expert. You must, must, must write your proposal for their benefit too.
* Remember that programme managers and panel members see tens or hundreds of cases for support, so you have one minute or less to grab your reader's attention.