My man, get yourself some dash attack.
Dash attack is really good because the final hit of the move can combo into your forward air strings. If you aim to hit them with only the final hit, even if you miss they will struggle to punish you for it, as the move is quick to end and thanks to its considerable range, you haven't put yourself in range of the opponent's attacks.
Low(ish) risk, high reward.
Now to get around dash attack, your opponent can either shield, jump, or roll basically.
If you notice that they start to shield it a lot, you can start going for the big stuff with those grabs. If they start jumping a lot you can either challenge their jump with on of your own aerials (forward aerial is particularly good for this, at higher %s up air will take stocks), or if you don't want to take that risk, aim for their landing. Try to stay under them and shield if they are coming down on top of you so that you can grab them (or neutral air them), but if you find you can't grab them because they are moving too far away, you can use dash attack instead to hit them as they land. This is really good against characters who outspace you, such as Marth.
Rolls are a bit harder, but if they roll behind you that's a grab or neutral air, if they roll away, dash a bit further and then aim to hit them with the last hit of dash attack again.
This is the the most basic principle behind approaching with Ness - it is a rock-paper-scissors type of game where you either go for some kind of grab, an aerial or a dash attack. Your job is to know which situations to use which one and then apply that to a game. It is also important to note that although all three options are equally important, basic maths dictates you will likely be using dash attack and forward air combined more than you will be using grab. Keep that in mind. This corresponds accurately with the basic risk-reward of each of these options.
This RPS game involves a lot of watching your opponent and a little bit of educated guesswork. For example, if you notice that they literally never shield and only either roll, jump or attack when you run at them, you can rule out dash grabbing, for example, and instead use a safer option like forward air or dash attack, which beats some of those options (you should know which by know) but doesn't leave yourself too vulnerable if you guessed wrong because you can do something else, like jab or shield, very quickly afterwards (unlike a grab, which leaves you very vulnerable if you don't connect with it).
You can't and shouldn't try to read the opponent 100% of the time, which is why safe moves such as forward air and dash attack are so important to the whole approaching game when playing as Ness. They let you test out how your opponent might react without leaving yourself too open, but give you high reward (a combo, for example) if you do land them. Grab has more reward, but it is also more commitment and it is a higher risk, meaning you will be more likely to get punished if you guess wrong with it.
Once you get the basics down... you can go much deeper than mere RPS to really mess with the opponent.
This is when you start going into baits and punishes, such as pretending to throw rock when you're actually going to throw scissors, perhaps by short hopping but not using an aerial (this is a really good way to leave the opponent open to grabs - fake them out with some kind of attack), or using moves like up air to approach (which takes a while to get the hang of but is really really good when used in combination with baits and such).
This game gets a lot deeper than simple rock paper scissors, especially when you start involving use of your shield to approach, as MegaMarioMan9 mentioned. Shield is a very good option, don't forget to make the most of it.
I'm not going to go in-depth on all of this here, because its just not practical for the sake of this question. Something you should take away though is that just because you can use an attack, that doesn't always mean you should. Sometimes it's best to hold back before just jumping straight into an aerial, dash attack or grab - you may find your opponent will do something that you can punish with a grab that you wouldn't have found if you Rambo'd him thinking "I've got to hit him NOW". Have a bit of restraint and a lot more opportunities will come to you.
You also need to remember that the opponent is obviously going to try to hit you, so you need to keep that into account. That's one reason why sometimes you're better off waiting for a second before trying to approach them - you may find yourself running into their attacks, or that you have been baited. I will reiterate what MegaMarioMan9 said again - use your shield.
Don't rely on just aerial/dash attack/grab, your shield is your friend and you should use it to protect yourself whenever necessary. Sometimes it will give you easy chances to grab the opponent (totally bypassing the RPS game we've discussed and making your life much easier) if they hit your shield with an unspaced aerial - just make sure they have actually hit your shield before going for the grab.
If you're reliant on PK Fire to get your grabs than this might be one reason why you can't seem to do anything - you're making it too easy for the opponent to hit you, so you rely on outspacing their hitboxes. By incorporating dash attack into your play, then, you can keep the advantage of PK Fire (the range of the move) whilst also giving yourself access to a much deeper approach game, as we explained right at the start.
Practice practice practice. It takes time to know the range of dash attack, judge when to dash attack to hit a falling opponent perfectly, and generally build a solid rock-paper-scissors whilst also trying to observe the opponent and not get hit.
But this is what makes Smash a good game. And this is what makes Ness a fairly decent character to learn the game with in 2018 - he gives you what you need but doesn't make it easy for you. It takes a bit of time and willpower to start with but if you put in the effort, you will gradually start to see results.
And if you forget everything else, just remember: use dash attack and forward air safely, and use your grab as the "scissors" option to compliment these two moves.
I hope this was of use to you - I'm willing to discuss anything further here or in DMs, just keep in mind that I don't use SmashBoards that much so I may not respond quickly.
