My problem is I don't know what's happening, I guess I'll try to figure out what's wrong with my grabs but for now I just can't time it right.
Well, I'll throw some stuff out. Let us know what sounds like it might be relevant, if anything. Someone else can probably be more thorough.
Two ways to grab: the grab button (z) and shield + attack (R + A)
Running grabs have some properties different than standing grabs, and usually feel like they have shorter range. On the flip side, you're moving while you do them, so you have more effective range covered. If that makes sense. If you do running grabs, try to do them a little early. I have trouble personally landing running grabs as Falcon, since the timing is earlier than I expect. Watch videos of your character to see the timing. Who do you play? Are you doing grabs from run or walk or shield?
One of the basic systems of the game is that shields beat attacks, grabbing beats shielding, and attacks beat grabs. You have to be in very close for a grab, so be careful if you expect them to put out a hitbox. Shield grabbing helps here. If you hold up your shield, when they get close and hit it with a move that has lag, press A to grab them. When you're wanting a grab from your own offense, try to condition them into expecting an attack, then throw out a grab instead. A common example of this (that doesn't always work because people) is to try coming down from above with an aerial. They'll shield and punish. If you then fall without doing the move, some people will still be waiting to get hit, and you have a shot at a grab.
But grab > shield is of course, not as simple and happy as that. Grabs can also be dodged from shield. While in shield, opposing players can dodge in place or roll to either side. In both cases, the solution is basically to change your timing. If they keep spot dodging, you can run past them and pivot grab, or run in from of them, shield briefly, then grab if they dodge. Overshoot/undershoot if you expect the roll.
Also be on the look out for slow attacks in neutral. If you opponent is fishing for Fsmash or something and you're close at all, a lot of the time you can run in and get a grab.