What are the best conditions for yeast to develop?

I don't find tanto quanto influence on flavor .vs. temperature as is generally claimed - I'd suggest running your own experiments on that front before assuming all that is written is utterly true. I do often drag out bread-making for days, but I don't find my "hurry-up and bake" loaves noticeably inferior, though they are somewhat different.

Once properly rehydrated (or improperly rehydrated, so long as it's not so improper as to kill it) dry yeast or wet makes no difference. My current version of "properly" is based IIRC on directions from Danstar for brewing yeast, but the baking yeast don't seem to mind - water (ideally boiled and cooled) at about 85-95F/30-35C sprinkle dry yeast on, don't disturb/stir/etc for 15 minutes, stir and wait 5 more minutes, introduce to food (flour) and try to avoid drastic temperature shocks. They will put up with much less ideal treatment, but if you exceed 120F/48C you may well finish them off.

I generally provide no sugar to baking yeast, following some book's advice to let them adapt to eating flour if that's what they are supposed to be doing. It works. I tend to delay adding sugar when making a sweet bread with this in mind. Yeast, flour and water should be all you need to get yeast growing. Salt inhibits yeast - some folks think it's vitally important, IME it's not.

When I need bread in a hurry I pull out all the cheats - I get all the liquid to roughly 100f/38c, I add sugar from the start, I knead the dough once (pretty throughly) when mixing and form it straight into pans, I put the pans in a warm (95F/35C) place to rise. It makes perfectly decent bread - try it sometime, you may be surprised. It's not my normal process mostly because it's more effort than my normal process and I'm often not in much of a hurry.

At the moment I have a batch going where I rehydrated the yeast in not particularly warm water which ws not boiled and cooled (and thus has chlorine in it being town water supply), forgot to get any flour to them before leaving the house for several hours, put some flour in when I got home, whatever yeast survived that managed to take off and multiply overnight, I baked part of it the next morning and added some more flour and water to what remained. It's been at 68F/20C more or less the whole time. Later I'll probably add a bunch of eggs, more flour and veer it towards something Stollen-like with some sugar, butter and fruit/nuts.

In my personal experience, yeast and yeast bread are remarkably adaptable and generally forgiving. "Best" really depends on what you want - a few days in the refrigerator is slow, but if it makes bread you like better and you have the time, it might be best. Most folks swear by that for pizza dough. Experiment.

Ecnerwal's answer is great. I'd add a few details.

I heard that there are two methods to develop yeast: in cold (which makes the dough taste better) and warm places (makes it develop faster).

Yeast fermentation, to my mind, falls into roughly five temperature ranges:

1. Above ~95F (35C) - Yeast growth slows down and there is excessive production of bad flavors. Don't ferment in this range. Going significantly higher may kill yeast.
2. ~77-95F (25-35C) - Yeast growth is fast, but there is more production of less desirable flavors (ammonia/sulfur as rumtscho notes, as well as odors that might be described as excessively "yeasty" or "beer-like"). This is mostly used when a fast fermentation is desirable or necessary, and it's best for enriched or flavored breads (with added sugar, oil/butter, eggs, other herbs/spices/etc.) which will mask the less desirable flavors. Sourdough ("natural" yeast) breads will often have even more substantial changes in flavor when fermented in this range, due to combinations of yeast and bacterial activity.
3. ~68-77F (20-25C) - This is often considered the "optimal" fermentation range for bread. It's fast enough so you can bake in a reasonable time, but slow enough not to encourage bad flavors while allowing some enzyme activity to release more good flavors. This enzyme activity is particularly important for "lean" doughs (consisting only of flour, water, and salt), where all the flavor has to come from the flour.
4. ~60-68F (15-20C) - This is the range sometimes advocated by artisan bakers for "slow" fermentation. The yeast develops more slowly, allowing more time for enzyme activity, as well as changes in dough structure. For sourdough breads, fermenting at a lower temperature can often lead for a more "sour" result, which some find desirable. The disadvantage is time.
5. below ~60F (0-15C) - These temperatures are generally used for "retarding" dough, rather than active fermentation. Again, they can be used to create more flavor or allow changes in structure and gluten formation. They can also be used for timing a bake while fermenting overnight or over a couple of days. Yeast will still grow somewhat down to refrigerator temperatures, but growth will be slower and slower.

I also heard that I should use sugar to activate it

Generally not necessary. Hydrating and "proofing" the yeast with warm water (and perhaps sugar) is not necessary unless you want to test it (i.e., "prove it") before mixing when you suspect the yeast may be old or defective.

Dried yeast granules also often package the yeast within a tiny bit of growth medium ("food" for the yeast), so even if you "proof" it, adding sugar isn't really necessary.

Do those depend on whether the yeast is dry?

At least in the U.S., "dry yeast" doesn't really need to be treated differently from other yeast in most cases. Decades ago, batches of yeast were less reliable and degraded faster, so "proofing" in warm water with a bit of sugar was recommended to ensure your yeast was actually alive. The sugar gave a more rapid response to see it bubbling and "prove" the yeast to be good.

Hoje em dia:

• Fresh yeast (or compressed or cake yeast) can usually be crumbled into small pieces and added to the dry ingredients or mixed with a small amount of liquid first.
• Active dry yeast supposedly requires rehydrating first in warm liquid, but modern versions of it can generally be mixed directly into the dry ingredients as long as it is mixed evenly and distributed well.
• Instant dry yeast is in smaller pieces and can be mixed directly into the dry ingredients.
• Rapid-rise yeast is supposedly better for "single-rise" recipes and for very fast breads, but experiments done by some professional kitchens haven't noticed a significant difference.

and some mention salt, though I have no idea for what purpose.

Salt inhibits yeast growth, and it also makes some changes in dough structure and gluten formation. It is sometimes useful for moderating (i.e., slowing down) yeast growth, to allow more enzyme activity and to prevent rapid dough expansion through excessive yeast growth before the dough structure has developed enough to support it. But the effect on yeast is relatively minor, and there are bread traditions in various parts of the world (e.g., Tuscany) which make bread without salt.

Anyhow, you do NOT want to add salt while proofing or hydrating yeast, since it will actually slow down yeast growth.

How to give yeast the best conditions to develop?

It depends on what you want. Recipes from a few decades ago often targeted the fastest possible bread from mixing to baking. In that case, fermenting at warm temperatures (range (2) in my list above) gets the bread to rise the fastest, and hydrating the yeast in warm water first may give it a slight head start to perhaps shave another 5-15 minutes off rising time (while also wasting 5-10 minutes to see it "proof"). However, if you really are that pressed for time, it might make sense to increase the amount of yeast in the recipe slightly.

If you're trying to maximize yeast growth rate, that's what you should do. But letting the yeast grow more slowly can allow changes in flavor, fermentation, and bread structure which might be valuable too.