Step 1: Set Leagues
First, you have to make sure you've selected the right league; if you don't know what league your character is in, check the character selection screen.
Step 2: Set Item
Now that we've set our search to the right League, we want to select what we're searching for. If you're searching for a particular unique item, enter the name of that unique item into the name bar. Otherwise, if you're searching for a rare item, select the type.
For this example, we're going to search for a good Divinarius, Imperial Skean.
Step 3: Check Possible Rolls
Now, if we're searching for a unique item, we should go to a resource that can tell us the max rolls for that unique item. I use Gamepedia most of the time. From this, we can gather data about our chosen unique.
We can see that the Divinarius can only roll two stats: Increased Spell Damage and Increased Critical Strike Chance for Spells.
Let's say that I'm going to prioritize Increased Spell Damage over Increased Critical Strike Chance for Spells, and I want my Divinarius to have a minimum of 67% Increased Spell Damage.
Step 4: The Search
Now we set our primary parameter to search only for items with a minimum of 67% Increased Spell Damage.
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Then, we're going to make sure "Online only" is toggled on. If it's not on, you might find it very frustrating while trying to buy an item. Next, let's put in the maximum amount we're willing to pay, which will be 4 Chaos in this case.
Now we're ready to press "Search".
Sometimes There's No Item That Fits Your Search
When this happens, it's time to go back and loosen up our requirements. First, let's make sure we typed in our rolls correctly; then, let's increase the max price to 5 C and decrease the minimum Increased Spell Damage a bit, to something like 65%.
Step 5: Sort Search Results
This time we've succeeded in finding 3 Divinariuses that satisfy our requirements. Now let's sort them out by our next desired attribute, which is % increased Critical Strike Chance for Spells. Click on that stat on one of the Divinariuses that are pictured below:
After clicking on that, you'll see that poe.trade will automatically attempt to sort the items by most desirable % of the selected stat; now we can see which one of the Divinariuses we like most by skimming the top results.
Step 6: Contact the Seller
Now that we've decided we like this Divinarius, we should try to contact the seller. Click "Whisper." This will automatically copy a buy message to your clipboard; if successful, it'll say "Copied to clipboard" instead of "Whisper." Now go back into your Path of Exile client and send the seller a whisper by pasting the message into the chatbox.
If the seller does not respond promptly, find the next best item on the list and send that item's seller a whisper too. Repeat until you get a response. Generally, responses on a current challenge league will be pretty quick; if the seller doesn't respond near-instantly, then it's likely that they are never going to respond. On the other hand, it may sometimes be very hard to get a response on Standard League, because many people have items for sale on it, but do not actively play it.