It may just look like pixelated anime characters sliding around on a grid, but Fire Emblem Fates has a lot going on underneath the handsome character portraits. The in-game guide covers most of the basics, and you won't need to think about stat growth percentages and ideal support pairings much if you're a new player on the lowest difficulty settings. That said, there are plenty more tricks and relatively unexplained features that should make your life as Matchmaker General much easier.
Your starting selections have lasting consequences
Picking your Boon and your Bane will not only alter your initial stats, it will also affect how quickly they grow for the rest of the game. Thankfully, they're all fairly self explanatory - if you want to be a melee bruiser (which is probably your safest bet) pick Strong or Quick as your Boon and Dull or Unlucky as your Bane. And make sure you select a fitting Talent, since that determines which class you'll be able to swap over to by using a Heart Seal later in the game.
Position your forces ahead of time
Your prep work shouldn't end with selecting your units and kitting them out. Positioning your army properly at the start of a battle could be the difference between an efficient assault and endless rounds of back-and-forth slaughter. Hit "View Map" before a battle and select your units to swap them around, or even pair them up. Stick your hammer-wielding brutes near armored opponents, put your lock-pickers near doors, and half (okay, maybe a quarter) of the battle is already won.
Watch those Dragon Veins
Dragon Veins do all kinds of things, and any royal character can use them. That means you can send your siblings out to summon a storm or healing aura instead of wasting your avatar's turn, but it also means your forsaken family members can use them against you. Make sure to check out what each (if any) Dragon Vein does by highlighting its square and pushing the "A" button. That will reveal both its action and the affected area. Then just make sure you never leave your buddy on a "maim horribly" square when your vengeful brother is nearby.
The enemy attack overlay is your best friend
For real, the first button you press in every battle should be "X". That will turn on a violet overlay that represents every map square your opponents will be able to reach and attack in their next turn (assuming no other units move into or out of their path). That way you can easily position your army just out of harm's way, but still close enough to move in for the kill. You can also select individual enemies and press "A" to see their specific attack ranges.
Hold off on using Master Seals
Almost all of the base character classes in Fire Emblem Fates can be upgraded when they hit level 10. It's tempting to use those Master Seals as soon as you can, since the upgrade comes with immediate stat boosts (not to mention a cool cutscene) and sets your troops on the path toward unlocking powerful skills. But it's usually better to let them hit the standard level cap of 20 first. This drops them back down to 1 for further leveling, and gives you more time to make sure you want to stick with that character (Master Seals ain't cheap). If you think a unit may hit 20 in the next battle, stick a Master Seal in their pack before you send them out!
Some characters just can't have relationships
I spent several battles trying to pair up a Nohrian resistance fighter with the crown prince of Hoshido before I realized their romance was even less likely than I thought. A quick check of the Support menu revealed that she can only have a relationship of any kind with your avatar, a solitary curse that also applies to several other units. It's fun to let your allies build relationships naturally based on who they end up fighting alongside, but make sure those telltale Support hearts pop up in combat if you're hoping for anything more.
Breeding is a great source of extra XP
Minor spoiler alert if you didn't play Fire Emblem Awakening: Fates, too, lets you recruit children born from certain S-rank character pairings. The kids have unique skills on top of those they draw from their parents, which makes them generally great additions to your party. But there's a less obvious benefit: each extra-dimensional teen comes with their own Paralogue full of enemies to squash. Birthright and Revelation players can always scout around to grind up levels, but you'll really cherish that opportunity for further leveling/item finding/support building in the scouting-free Conquest.
Your fort design isn't just for looks
There's nothing wrong with just sticking your fort buildings wherever they're most aesthetically pleasing. But if you plan on playing through the Invasion missions - or better yet, defending your Deeprealm claim from other players - then it wouldn't hurt to add some tactical foresight to your feng shui. Enemies will appear from the gates at the eastern, southern, and western walls of your settlement, so position defensive structures like launchers and puppets accordingly. You can take a peaceful visit to other players' castles if you need some quick currency for further fortifications.