Many job vacancies call for application forms rather than CVs, particularly in the public sector. Filling them out can be a time consuming task, meaning that it's best to be selective and only work on those for jobs you have a realistic chance of being shortlisted for. It is better to send off one or two carefully and thoroughly completed forms than to try and dash of dozens of applications.
The first and most important piece of advice I can give is to follow the instructions carefully. This sounds obvious, but it's surprising how often over the years I've seen instructions on application forms misunderstood or ignored completely. This has ranged from flagrant disregard - writing "see CV" across the Experience section instead of listing employers and dates - to the less blatant - writing in the wrong colour ink or leaving off past salaries or reasons for leaving.
Ignoring or misconstruing the instructions is likely to get your application form put in the 'no' pile on first pass, simply because it demonstrates quite obviously to the hirer that you can't follow instructions! Whether this is through slopping reading/misunderstanding or wilful disobedience/'I know better' attitude, either are large red flags for someone wondering whether to hire you.
The second area that causes greatest problems with application forms is the large blank box apparent on most of them, headed by a question something like "Describe your suitability for this post, referring to the requirements of the job description/person specification".
Since the JD/PS is likely to have a list of required criteria or competencies in it, it is best to create headings in the application form box and write paragraphs &/or bullet points under each one. You should make sure you address them all, both the essential and the desirable ones. You need to give one or more examples in each case, as evidence to demonstrate that you have that attribute.
One of the commonest mistakes that I've seen is to write one or two sentences that boil down to "Yes I've done x, I'm very good at x". This will score minimal points in whatever system the hirer is using. Instead, you need to show and not tell. That is, you need to describe a time when you used that skill or competence. It is fine to use an example from outside of work, for example from a club/society, professional association or leisure activity.
The best way to give the examples for each criteria is to use the STAR technique. This stands for Situation, Task, Action, Result. Start with a (brief) description of the context, and the task you needed to undertake, then describe in a bit more detail the action(s) you took to do it, and the result or outcome. It's fine if the result isn't a positive one, so long as you add a reflective sentence explaining what you could do differently next time or what you learned from the experience.
Once you have completed your application form it's a good idea to print it out (even if you will be submitting it electronically) as it's easier to proofread it in hard copy. It also allows you to ask a friend or family member to proofread it for you as well. Ask them to check that you've addressed all the criteria as well as look for spelling or grammar errors.