The first time you open Path of Exile 2's Trade Site, it can be overwhelming, but after this guide, you'll feel more confident using it. Many of the extra sections will be hidden but can be expanded by clicking the button to the left of the words to reveal additional boxes to improve your search:
Let's break it down section by section.
Search Bar, Type Filters and Stat Filters
Search Bar
At the top of the Trade Site, you will see a search bar with the words "Search Items...". In this section, you can type the exact name of any item in the game that you wish to buy, from Uniques, to Currency Orbs, to item base types.
League Selection
To the right of the main Search Bar you can select the League in which you are playing. This defaults to Standard but can be changed to Hardcore or another League of your choosing
Online Only
Allows you to only show results from people who are currently online and in game, but can be changed to show results from offline players too
Type Filters
Item Category
In this section, you can select the item base type you're searching for. For example, you could add in "Two-Handed Mace" to only show results for that item type
Item Rarity
Allows you to only bring up results for items of a specific Rarity. This can be useful either to find Unique items, or if you're looking for a Weapon with certain mods, but need it to be Magic Rarity because you intend to use a Greater Essence on it
Item Level and Item Quality
These fields allow you to specify a minimum and/or maximum Item Level and Quality range for search results. This can be helpful when searching for item bases that have to be a specific Item Level to be able to attain certain mod tiers, or perhaps you're looking for a Skill Gem that already has 20% Quality before you buy it
Stat Filters
The Stat Filters section is the most important section of the Trade Site as it allows you to search for exact modifiers you want. Knowing how to use this section will make you able to find the exact items you want far more easily, as well as price-check items you have found and want to sell.
Clicking "+ ADD STAT FILTER" allows you to select any item modifier in the entire game. If you're searching for a new pair of Boots and need Movement Speed, Maximum Life, Fire Resistance and Cold Resistsance, you can add in each of these modifiers to show results that match your criteria. You can type in the modifier name to bring it up, or scroll through the list of mods and click the one you want.
You can also specify a minimum and/or maximum value range for each of these mods, so if you need exactly 37% Fire Resistance to make sure you're Resistance-capped in game, you can add this value
FUZZY SEARCH
THE MOST IMPORTANT TRADE SITE TIP OF ALL!
The PoE 2 Trade Site defaults to a very strict search -- if you don't type the exactly correct word or word order into any of the fields, no results will show up. However, you can force a "fuzzy search" by typing a tilde (~) at the start of any search to have results show up even if you don't get the exact order of words correct.
For example, if you wanted to search for Fire Resistance, instead of typing "Fire Resistance" you could type ~res fire. If you wanted to find Movement Speed you could even type something as simple as ~ent spe. This can also be applied to the Search Items field at the top to bring up specific items that you may not remember the exact wording for.
Stat Groups
To the right of Stat Filters, you will see a little box with a small pencil icon in the top right corner. Clicking this will bring up fields that allow you to further specify your search. You can add multiple Stat Groups to a single item search, allowing for very specific searches
And: Suggests "And I want ALL of these modifiers on my item". The Stat Filters defaults to this
Not: Will prevent any items with the selected modifiers from showing up in your search results. This can also be quite useful
If: Will show items with this modifier but only IF it has modifiers within the range specified. For example, "I want Fire Resistance but only IF it has 20-30% Fire Resistance, otherwise don't worry about it and show me items with all the other modifiers I want too"
Count: Allows you to specify that you want to find items with either a minimum number of selected modifiers, or maximum number of selected modifiers. For example, you might be searching for Jewel and there could be a dozen different modifiers that are useful to you. By adding all of these dozen mods to the Stat Filter and then selecting "Count" and setting the Minimum to 2, all search results would bring up items with at least 2 of the desired modifiers
Weighted Sum and Weighted Sum V2: This is a much more advanced Stat Group that will allow you maximum control, but won't be useful to the majority of new players. GGG themselves explained it best: "Adding a Weight number to an item will add a multiplier to its range which you can use to either search for a specified Weighted Sum or sort into a sum of your choice (after you've confirmed the search).
For example, adding a Weight of 1 to +# total to Strength would mean +10 to Strength would be 10 towards your Weighted Sum. Adding a Weight of 2 to +# total to Dexterity means +10 to Dexterity would be 20 towards your Weighted Sum and etc."
Source: https://www.pathofexile.com/forum/view-thread/2988324
Remember that you can combine multiple Stat Filters together to further specify the item you want to see. For example, you might have a search that suggests "I want Boots with at least 100 Maximum Life, 25% increased Movement Speed and then two Resistances of at least 25%, but it doesn't matter exactly which Resistances" which might look something like this: