To a beginner, all normal moves can look similar. Special moves are usually very obvious in their function, throwing fireballs, moving across the screen, invincible anti-air, but normals are more subtle. Specials usually have some type of trade-off that makes them very risky to perform, despite their high damage and powerful priority, such as being unsafe on block, taking a long time to recover, being slow to start up. If all you use is specials all the time, then you end up creating big weaknesses that can be exploited fairly easily. So that leaves Normals.
Normals can be broken up into a few categories: Jabs, Pokes, Sweeps, Anti-Airs, Pressure, and Overheads. The three that are most important for neutral are jabs, pokes, and pressure. Some normals can fit a few of these roles.
In general, there's a relationship between moves, moves that hit closer to your character have more frame advantage and start up faster. Moves that reach out further have less frame advantage and start up slower. So close up moves that come out quickly are usually good for pressure and damage, and longer poking moves are unsuited for when you're up close. Moves always have more frame advantage on hit than block, so if you land a hit, it's always your turn, and if you get hit, it's never your turn.
- Jabs are unique. They're your fastest moves, and recover the quickest, so they're really low risk, but they have a short range. They also self-cancel in most games, so they combo easily. If you want to get an attack out as fast as possible, pick a jab, usually a crouching jab. Jabs usually get good frame advantage, but deal way less damage than the next strongest attack, so while jabs are likely to beat whatever your opponent does, assuming they're in range, they aren't going to deal a lot of damage in the process. Your opponent can usually deal more damage with a single medium attack than 3 jabs. Because jabs have a short duration, frame advantage, and low pushback, this makes them good at Tick Throwing.
- Pokes are pretty self explanatory, they're attacks that reach really far, but they don't have any frame advantage on hit or block, so you want to hit them at the tip where your opponent can't retaliate. These moves keep your opponents out of your space, or you can time them to hit your opponent right before they poke to get damage on them.
- Pressure is kind of abstract, but it basically means all your close-up moves that are stronger than a jab. These moves start up a little slower, but deal a lot more damage, and are used for your stronger combos. If you can combo off a jab, it will usually deal less damage than one of these moves.
- Anti-Air is a move that reaches up above your character's head in some way, an uppercut. Not all characters have a move like this, so they need to either improvise, or go for air-to-air. Since jumping attacks can only be hit by moves that reach upwards, jumping tends to be a good way to beat most ground moves. Having the ability to shut down jump-in attacks is really important for this reason.
- Sweeps are like pokes. They hit low, have a long range and knock the opponent down, but are unsafe on block. Knocking the opponent down means you can then pressure them when they wake up by using a meaty attack. Since sweeps are usually unsafe, it pays to space them properly, making it so the pushback pushes your opponent out of range to retaliate. If your opponent does not space their sweep, your sweep usually has enough range and speed to punish them in most games.
- Overheads are slow to start up, overheads are safe on block. They need to be blocked standing, as they will beat crouch blockers. They usually have the character move a limb in a downward arc over the head of their crouching opponent. Throw these in to make the opponent think twice about the direction they block. Overheads are slow so it's possible to react to them.
Coming from a Street Fighter perspective, jabs tend to be LP or LK. Pokes tend to be MK. Pressure tends to be MP. Anti-air tends to be Crouching HP. Sweeps tend to be on crouch HK. Overheads tend to be a command normal, assuming your character has one at all. Standing HP and HK are wild cards and could potentially be any of these. The closer to you and faster a move comes out, the more likely it is to be cancellable, unless it's a crouch MK, which is frequently cancellable anyway.
When you pick up a new character, try grouping the normals into these groups. Also check up the frame data chart for what's plus and minus on block, so you know when your turn is, and when your opponent's turn is.
If you apply the rule of "short range = plus, long range = minus", you can generally guess what your opponent's frame advantage is on block just by seeing the move instead of needing to look it up. If you don't know however, Street Fighter V's training mode has a built in mode, Colors Frame Advantage, which displays who is at frame advantage after each move (blue is plus, red is minus, purple is even). Mortal Kombat X and Injustice now have frame advantage for every move listed on the pause menu. And of course these resources are available online for every game.