If you are new to FFT: Arena, please take a look at the Master Guide
to familiarize yourself with the rules, since that's what you'll need to work around as you build your team. Worry about stats, abilities, and items later.
When I build a team, I always start with an idea. I like to look through the list of abilities and equipment for inspiration. An excellent way to gather ideas, especially for those new to team creation, is to watch videos. Videos are great sources of ideas and concepts – you can get a feel for not only what works and what doesn't, but also for AI behavior. Once you have your idea, start thinking of other units and abilities that would go well with it, and work from there.
General guidelines when actually constructing your team:
1. Stick to your plan. Make sure each unit can do its job. You only have 3000 JP, and since each unit will most likely dabble in 3-5 jobs, you really only have ~2000 JP to spend on abilities. If you want your unit to have good R/S/M, said unit probably won't have many action abilities, and vice versa. Whether you choose to focus on explosiveness or opt for more stability and resilience (ex. status protection), make sure your team can carry out the plan.
2. Try to build a cohesive, synergistic team, not four individually strong units that are unfocused as a team. My S3 team is a good example of this problem. It was composed of four solid units, similar to my fairly successful S2 team. I was eliminated in the first round. Elemental absorb teams (popularized by the success of the S3 finalists) are a simple, straightforward way to have a team work together. Make sure the healing is worthwhile though – quite a few teams in S4 are capable of elemental healing, but it typically isn't enough to offset the damage by the opponent. Pride's “Return of Another Boring Team” and The3rdOracle's team are examples of elemental healing done right. Another fairly common example is the Lore + Save teams from older versions of Arena. Constant, low damage from the Lore user would power its teammates to absurd speeds and damage capabilities.
3. Revival and healing are good. Obvious, yes, but absolutely essential. At least one person needs to be able to heal and revive on a team. I don't remember any decent teams with no revival, or if anyone even had the guts to try a team with no revival.
4. Speed is good. More speed → more turns → more chances to make your opponent sad/mitigate any problems your opponent has inflicted. Haste is quite valuable – in AI tournaments, ~70% of teams will have someone that can apply Haste. With the recent change to Haste (increases speed by 25% instead of 50%), it will not be as important if you can't fit Haste into your team. Haste will only increase the effective speed of most units by 2-3 instead of 4-6. Slow, however, remains a 50% speed penalty, and is still rather crippling when applied at the right time. If you test against The3rdOracle's winning team from S3 (and/or Akwikone's resubmission of said team for S4), you will likely find that once Slow lands, any chance of comeback is instantly erased. That team runs on speed – the Hasted thieves are already fairly difficult to keep up with. Slow makes it impossible.
As for AI behavior, if you watch videos and test, you'll get familiar with it very quickly. If you've played FFT before, you already know a tiny bit about it! Now it's about manipulating it to do what we want. Here's how it tends to behave:
1. Be stupid. It's the AI. It'll somehow find a way to make you sad with their awful decisions, guaranteed.
2. Revival/healing is top priority. Always. Even if they could kill the last opponent (I'm pretty sure, anyway). If they think someone needs to be healed or revived and they can do it, they will. End of story. A rather extreme example that stands out in my mind, was I believe a match in S2, I think Dol vs Saeru. A geomancer had an opportunity to kill two units on the enemy team, but chose to retreat and revive instead. That move likely cost the team a victory.
3. Will almost always move and act, even if moving is unnecessary. The one exception is when they're at the end of the map, like in my match vs Skip Sandwich (S1, round 2)). The Lancer waited in place after throwing Phoenix Downs. They also like to act then move; rather frustrating when instead of Chakraing himself and his low-on-MP mage, the monk acts first, healing only himself, then moves next to the mage anyway.
4. MP restoration is erratic. Sometimes they'll throw that Hi-Ether on the Wizard when she needs it, and other times they'll ignore the Wizard and let her go whack the enemy for inconsequential damage and trigger their Speed Save. Most mages will have Move-MP UP to prevent them from becoming useless if they never get MP from their allies. In general, you'll want your units to be self-sufficient.
5. AI loves Haste, but hates every other buff. Absolutely loves Haste. If someone doesn't have Haste, they'll try to stick it onto them. In critical? Run away and Haste yourself. Other buffs? Not so much. Protect and Shell will only be cast after someone has been hurt, but at that point, they'll likely need to be healed, instead. Regen is considered healing, so they'll use it when in critical and have no better way to heal (say, a male Samurai with Masamune). Reraise? Forget about it. It's 100% hit in Arena and they still won't use it. Maybe if they're in critical. That's when they would use Preach in 1.3.
6. AI targets lowest HP units. They also like to waste actions – ex. a Lancer jumps on a target for enough to kill, but while he's in the air, a teammate kills the target. Lancer lands on corpse, action wasted.
I'm sure there's more, but these should be enough to take into consideration while you make your team.
"Know the AI, be the AI, kill everyone else!" - philsov
Suggestions? Any other topics I should address?