Disclaimer: Make sure you can actually use the FULL length of your initial dash. Use short dashes, long dashes, fox trots, pivots...everything.
Working your dash dance game is the right idea. Just try to think about what you're threatening with a dash dance.
Fox's threats out of dash: shine, nair, upsmash, grab.
Now try to think about what ranges your opponent can react to you running/jumping at them, and what ranges they can't. Learn those ranges.
So now the trick is to dance in and out of those ranges, and think to yourself each time you dash into that range "So I *could* theoretically nair at him right now, what is he doing to stop me from doing it?" and then dash out of that range, while watching their response. If your opponent is good, they will generally toss out some sort of counter, like an ftilt with sheik, or a WD back. The trick is understanding which ranges are not reactable for your opponent, and which ranges are. There's no use nairing if they can SEE you jump into the air, and just dash dance grab. You want to do it at a range where by the time they can see you dashing into your jump, its too late to do anything besides maybe shield at best.
So if you learn to recognize these ranges, and you learn to see each of your dashes forward as a threat for that...what next?
Well, learning how to get into those ranges! Here's the tricky part, because you want to get into these ranges in sneaky ways, or a good player will be able to recognize "oh, he's about to be at X position, where I can't deal with him well, let's DO something about it." Doing something about it could mean preemptively intercepting your forward movement, it could be giving you stage space, it could be jumping away, it could be setting up a wall...it could be a lot of things.
So there a lot of basic tricks to get into these ranges, but ultimately it's going to be more about understanding the flow of the match, and what your opponent is and isn't reacting to. For starters, here are some basic tricks:
1) Simply varying your dash dance length, for example: Do shorter dash dances outside of SH nair range, then one time use your full initial dash to get into SH nair range. Most people will think you're actually going to nair, and have to account for it accordingly, at which point you can bait them with a dash back since you're still in your initial dash.
2) Empty SH forward. Do this from pretty far away, so that you're still safe. People will have to react to your jump, but you'll land with no lag (or at least, only the normal 4 frames of lag), so it can be pretty tricky. You can empty SH and land outside of SH nair range, and then transition into another mixup (for example, empty SH into right outside of the range, then use example 1) from above to get in on them. Alternatively, you can be near, but outside, a good range to running shine at them for example, but then SH INTO that range.
3) Undershot nair. You can nair and purposely land at a range they can't actually punish. This gives them a visual cue to react to, without generally putting you in any direct danger. This means that you have a somewhat safe way to break the "normal neutral game" so to speak.
4) My favorite: WD in place. Just run up to them, then WD in place outside of the range of anything threatening-->observe what they do, use it as information for next time. As I said at the beginning, they have to theoretically respect you just running at them and shining, or nairing at them. Use that to your advantage to stop outside of their range, using your dash or full run as a visual cue. This is less likely to get you an immediate hit (unless you're a bit riskier, and WD in place RIGHT outside of range of a sheik ftilt, for example...in which case if they ftilt you get a free hit), but its far safer than the other tricks. In addition to being safer, it allows you to position yourself very precisely (something you can't do while dash dancing, because you'll always have momentum from a dash and reset your momentum. This allows for a more planned and calculated approach, and can at any point flow into any other movement option.
Hopefully that helps!