Conducting a trial is difficult and takes years of training and practice to do well. It is almost always best to have a lawyer acting for you should you be involved in a trial but sometimes that just is not possible. Legal aid does not fund every case and sometimes a lawyer's fee is simply unattainable. Recognizing that, people do go to court and represent themselves.
In the event you do represent yourself, expect the judge to ask you (probably well before the trial date) if you are planning to get a lawyer – don't take that as an insult and feel free to let the judge know why you don't have a lawyer.
The judge is always called Your Honour. If you are appearing before a Justice of the Peace you call the Justice Your Worship.
Before going to trial ask yourself what is the case about? What do I need to show in order to win? If you are seeking child custody you will want to be able to show the child will be well treated by you and you have a good plan for raising the child – maybe some photographs of your house and the child's room make sense. If there is an allegation that you would be a bad parent for custody – maybe you had a drinking problem – it would be a good idea to be able to show you took counselling and do not drink any more. Certificates of Completion of a counseling program may be helpful.
Whatever the case is about think it over and get the evidence you need that relates to the case – the fact the other is, say mean and nasty, seldom means much. Whatever documentation you find you should send to the other side and be able to prove you sent it (this last rule does not apply in criminal cases – but unless there is some good reason for surprise it probably makes sense to send it in criminal cases too). It hurts to be "helping" the other side but do it and the Court will see you are responsible and respectful.
Make sure you have completed all the paperwork needed and make sure it is filed with the Court well before trial. In a spousal support matter, for example, you will need to complete financial statements – make sure you do so and get them filed.
One final point before we turn to trial itself, there are complex rules of evidence that must be followed. You likely will not be able to learn everything unless you go to law school but one really important rule is the hearsay rule. Basically it means you cannot tell the Court what someone else said – you need to have them come and speak for themselves. So, if you have stopped drinking and your boyfriend can say he has seen a real change in you and that you are not drunk all the time you will need to have your boyfriend come to court and testify to what he has seen.
On the day of trial come to Court early; do not be late! Dress respectfully; if you have formal clothes wear them but if you do not then wear clean neat clothes without any slogans on the top. Court is serious and you want to be seen as serious. When you get into the Court itself (if the judge is not there) go up to the registrar (who will be sitting at the front) and identify yourself and explain you are here. The registrar will likely tell you to wait until your case is called. When your case is called go to the front and introduce yourself to the judge ("Your Honour, my name is XXX and I am the YYY [defendant/plaintiff/applicant/respondent whatever]"). Always stand when you are speaking; that does not apply if you are disabled but everyone else stands when speaking. Generally, if you are the plaintiff or applicant you sit on the right and the defendant or respondent sits on the left.
The trial then begins with opening statements. You give a very very brief description of your case and what it is about and what witnesses you expect to call. Your opening statement should not be much longer than ten minutes at the most – mine are often five minutes.
After opening statements are done, the testimonial phase begins. This is when witnesses are called to testify. First, the plaintiff or applicant calls witnesses for direct examination; in direct examination the form of questions should be open (who, what, where, when and why). If you are testifying yourself it is totally fine to just tell your story in your own words. Be slow and take your time. You can take notes with you to make sure you cover everything but the other side will be entitled to see the notes so its better to try to avoid that. Obviously if you will be referring to documents – say a lease or that kind of thing, you can take those up and refer to them. Make sure to give a copy of everything you mention to the judge to become an exhibit – you should make multiple copies of everything you intend to refer to. . At the completion of each direct exam, the other side can cross-examine the witness; during cross examination you can ask more focussed questions ("isn't it true that XYZ"). The process is repeated until the plaintiff or applicant is done calling witnesses. Then the defense or respondent calls witnesses and the processes repeats.
After the testimonial phase is complete you get a chance to summarize your case. You want to be clear and to point out whatever came out during the trial that helps your case or hurts the other side. Be polite and sensible. Extreme language wont help!
One final tip – if you can, go to court and watch a trial or even part of a trial. It helps to see all this in action!