It is weird that you are not going to mediation before the custody trial ,,
Usually mediation is first ,, then if parties can not agree on custody arrangements then it goes to trial
Mediation is set where a mediator ,the 2 parties, and sometimes lawyers all get together and try to hash out any custody disputes and terms of custody ..
In an actual trial you are there with your lawyer before a judge with what you want for custody and why you want those things .. You are there to prove your case,, take with you any documentation to help your case, any witnesses to testify on your behalf ..
Dress nicely and be very polite