As the title says :)

You have to find special locations. No need to hurry.

Explore. That's what the M&M are about.

The thing is though, I found a well under Dusk that increases my speed. but my stats are the same. I was wondering if maybe the game doesn't actually show the increase?

Oh I'm not worthy! Better rescue those prisoners.

If it's like MM2, each stat actually has two values:
1. The current value, which is what is actually displayed on the screen.
2. The base value, which the current value will become after a battle or rest.

It is possible that the fountain may only increase one or the other. If it only increases the current value, it is only a temporary benefit. If it only increases the base value (yes, this does happen), the increase won't show up until you rest or finish a battle.

Also, note that fountains that increase the base value could fail to work if you have used them too frequently, or if the stat (probably base, but you never know) is higher than a certain value. (The latter mechanic is actually used quite a bit in the series.)

One more method that works in MM2 and is worth trying in MM1:
1. Equip a charged item that provides a stat boost when equipped.
2. Use up the item so that it breaks.
3. Unequip the broken item.
In MM2, this gives you the stat bonus permanently (though there is another bug that can make step 2 impossible in certain cases). If suitable items exist in MM1, it's possible that trick might work there.

Okay, by "You are not worthy" my alignment was too low. So I raised them all to good.

My Sorcerer for example has 11 speed. Wasn't raised immediately after, nor after a battle or after resting.

I don't think worthiness has to do with alignment, actually. That confused me a lot as well when I played. But I figured out what it means later. If you keep exploring for a while, you'll eventually work out what the whole worthiness thing is about.

What I think happened is that your characters had their base speed raised but this didn't show up until you rested. At least, that's how it worked when I played. Your characters should all have their speed boosted now, if you've rested since you found that location under Dusk.

I just said though, after I rested nothing changed. Unless it already added the stats the first time and I somehow missed that, and "only" does it once.

And when I first went there it said "You are not worthy" until I restored my alignments. Then it stopped saying that. (I think you're thinking of the Giant Statue near Dusk, which says I'm not worthy until I rescue all the prisoners)

You can't use the stat raising locations several times in a row, they only work once, leaving the area and returning won't reset them either.

It does only do it once. I'm trying to avoid spoilers... I know how the stat boosting locations work, how it relates to whether you are worthy, and I know how one becomes worthy, but I don't want to spoil that. But it is not related to the giant statue near Dusk, that's something else.

Okay thanks :)