Strengthen your bargaining position by knowing exactly what theories of liability you think apply, and anticipate all the defenses the other side will use, and why those defenses are either strong or weak. This will be a roadmap of leverage points you will be using during mediation to make your argument as to why the other side should acquiesce to the relief you are seeking.
DO use demonstrative aids
If you are a plaintiff, consider making a short video that educates the defense regarding the extent of the injuries, or that even interviews survivors to a wrongful death action. If you are on defense, consider sharing verdict outcomes for similar cases, or distinguish how this case may not result in the demand requested.
DO understand mediation confidentiality can work against you
Mediation is a settlement proceeding, and as such, many laws typically tend to prohibit anything that was said at mediation from being used in open court. In other words, just because the other side came up with a figure in mediation you almost liked but ultimately refused, does not mean you can bring it up in court if mediation ends up failing. Thus, take all mediation offers seriously, and don't think you should refuse just so you can bring up the offer later in court. The court may refuse to hear evidence that the other side was offering better settlement offers in mediation than in court.
DO be on the lookout for enforcement of settlement discussions
There are times where you may have agreed upon something with the other side in open court and have decided you would like to backtrack. However, the other side may file a motion with the court to have that part of the settlement enforced. Be careful not to agree to anything, orally, or in writing, in the jurisdiction of the court, without being sure 100% that this is exactly what you'd like.
DON'T abuse the mediation process
Many participants go into mediation, not expecting to settle, but just to gain more discovery opportunities to see what cards the other side holds. If you engage in this practice, you may force the other side to harden its position completely, and you may lose out on a settlement offer that could have benefited both sides.
DON'T agree to turn the mediation into arbitration without knowing the risks
Some mediation participants may have come to resolution on some issues in a matter, only to agree to have the mediator turn into an arbitrator to resolve the last few or one remaining issues with binding authority. The problem that may occur is that the mediator turned arbitrator, now as an arbitrator, has information gleaned from the mediation he may not have had access to before. As a result, the mediator in one fell swoop can now as arbitrator, decide against you completely on an important last matter.
DON'T overburden the mediator
Some participants, before a scheduled mediation begins, like to fax thousands of pages of exhibits to the mediator. Aside from forcing the mediator's fax machine to run out of ink, this may cause the mediator to run out of patience. A "mediation brief" is supposed to be, as the name suggests, brief.
DON'T give up
"Blessed are the Peacemakers" and other quotes come to mind. Most cases (up to 95%) never see trial. If you've made it as far as mediation, always give yourself a pat on the back and realize that you are empowered, with the other side, to come with a resolution of your own crafting, rather than being forced to abide by a decision made by someone else on a bench, who even though presumably wise, will never know your facts like you do.