Make a Quicksheet
You don't need the full rules, just the ones you use a lot. A short, 1-2 front & back sheet of paper with the important references. The value of this isn't just reference, it's because it's a thing for the players to look and fiddle with while they're playing - sometimes you need constant exposure to get things through. But it also means that whenever it comes up, you can point to the spot on the Quicksheet and go, "And here, we can see this rule works like X" to get it ingrained in their minds where to look.
Walk through the steps until things click
"Make an Intelligence Save against DC 14."
"I can't find it on my sheet."
(grabs a sample character sheet) "Ok, Saving throws are adding your Intelligence modifier (points on sheet) and your Proficiency bonus (points on sheet) and if you meet or beat a 14, you succeed."
You'll need to do this a lot. It's useful for new players in general, but they pick it up quicker because they're not defaulting to ingrained habits from before.
The other value is that other players will see this and it slowly absorbs for them, as well.
First, the specific case of Alter Self. The Natural Weapons feature of Alter Self explicitly modifies your Unarmed Strike. So if your Unarmed Strike is not a finesse weapon, that doesn't change. This is covered pretty thoroughly in this answer.
However, the general case of 'Do natural weapons have the Finesse property?' is much less clear cut. Take the Raven (Appendix A of the Monster Manual). The Raven has a Str of 2 (modifier -4), a Dex of 14 (modifier +2), and, from the 'Proficiency Bonus By Challenge Rating' table (page 8 of the Monster Manual), its proficiency bonus is +2. Its attack bonus with it's natural weapon (beak) is +4. So it seems clear that it is using
Dex bonus 2 + proficiency bonus 2 = +4 to attack.
There are numerous examples along the same lines, but I chose the raven because the difference between its Str and Dex makes it pretty clear that it's using Dex.
On the other hand, we have the Mastiff. (Also Appendix A of the Monster Manual). It has a Str of 13 (modifier +1), a Dex of 14 (modifier +2), and the same +2 proficiency bonus. Its attack bonus is +3. So it appears to be using
Str bonus 1 + proficiency bonus 2 = +3 to attack.
The Mastiff is not nearly as good an example, but every creature I could find with much higher Dex than Str uses Dex to attack.
Based on these (and a lot of other) examples, it seems clear that some creatures can use Dex to attack with their natural weapons, but some cannot. Alternatively, it's possible that creature attack bonuses are either arbitrary or not calculated the same way as humanoid attack bonuses are, but if this is the case there is no way to answer this question outside of the specific case of Alter Self.
Best Answer
D&D 5th edition was designed with something its designers call "bounded accuracy." A full description and analysis would require more text than is appropriate for this format, so I recommend a search of the topic on the wider internet.
To very briefly summarize bounded accuracy, all modifiers (and also target numbers, such as AC) in 5e are limited to a range that is much smaller than previous editions. One of the main results of this is that a large number of very easy monsters, such as goblins, are still a threat to a party of high-level adventurers. This is different from the last few editions, where a single high-level character could defeat an almost infinite amount of goblins.
Too large of bonuses from magic items would break this desired mechanical behavior, while smaller bonuses are more significant than in previous editions.