1. Always tell the truth: I can't go on about this enough. While I acknowledge that there are things in your past or present that might complicate your visa application, there is no point hiding information, especially when this information can be obtained sooner or later by alternative means. It is far better to tell the truth, face the issue head-on, and explain why the circumstances as described do not disqualify you from due consideration for the visa in question. The easiest position to defend is a truthful one.
2. Do your research: Ensure that you understand all there is to know about the visa you're applying for. This may sound obvious, but I have known many to submit visa applications with thoroughly inadequate preparation. You should know the purpose of the visa, what you're allowed to do when travelling on that visa and what is expressly prohibited. You should know what key things you will be required to prove in order to qualify for the visa, and what documents you must submit. Once you understand what you are required to prove, you can be more intelligent in preparing your documents and submitting over and above what you've been asked, if necessary to prove a particular point. For example, if you understand that you need to prove your ability to sustain yourself for the duration of a 3-week holiday, you will be in a better position to know that it makes no sense submitting bank statements which have no money in them.
3. Review your documents: Once you have researched and are sure of all you need to take with you, be sure to review your documents before submission. Ensure that you have all the documents you are meant to have. Take note not only of the documents (i.e. I've got my bank statements), but of what they contain (i.e. do the statements reflect the amounts and dates that they should). Look out for missing information and ensure that all corrections are made before submission.
4. Ask yourself the hard questions - and answer them: Put yourself in the shoes of the immigration caseworker and ask yourself the questions you think he or she would. Is there a glaring hole in your application? Make it your job to anticipate all the hard questions the caseworker might ask when reviewing your documents. If you will not have the opportunity to attend a visa interview, then ensure that you answer the questions in a covering letter. Do not just leave hard questions unanswered, hoping that they don't get raised. The absence of an answer could result in the refusal of your application. I'm not suggesting that you shine a spotlight on every little crease in your application, but that you face the issues that are, on the balance, going to raise questions in the caseworker's mind. If you will have the opportunity to speak in person, you might want to think more about what you will say in response to the hard questions. Prepare, as you would for a speech or a debate. But remember number one. Tell the truth.
5. Submit your application in time: This applies particularly if it is an in-country visa extension application (e.g. a UK visa extension applied from within the UK). Such applications typically have to be submitted before your previous visa has expired.
6. Abide by your visa conditions: Once your visa has been granted, make sure that you abide by the stated conditions. This will increase the chances of your next visa application being successful. If you breach the conditions of your stay, this could adversely affect future applications, even applications to other countries. Referring back to the second point, ensure that you know all about the visa and what you're allowed to do when travelling on that visa, so that you do not unwittingly fall foul of the rules.
I hope you find these tips helpful. Good luck with your visa application!