[Steam] How do I buy a gift NOT for myself (to create a giftaway here?!)

Find a game. Make a giveaway. Add the person on Steam. Select product on steam and add to cart. Click box on right side to purchase as gift. Select person's name on list. Add message. Pay. Mark send.

Something like that, though with regional pricing you need to be sure that you can actually give the game and not have too low price on your end.

You really can't. The biggest problem is regional pricing. If you buy the game and the winner is in a different country, they won't be able to receive it due to regional pricing.

Make sure the price difference in your currency is not < or > 10% on the currency of the winner

So first of all I need to find / wait for the winner, right?!

The easiest way would be to buy games, not from steam, but from legal sites, like fanatical, bundle or so.

As others mentioned region pricing on Steam can be a pain for some. Since you live in Ukraine what you could do right now is attempt to buy the game you are thinking about using for a GA to friends in other regions on Steam without actually buying it. Then you would have an idea of what region lock tags need to be applied when creating your GA. The least troubled option would be to make the giveaway just to your region as you more than likely wouldn't run into any issues when giving it to the winner. Also if you are waiting till a Steam sale comes up it's best to make the GA at the start of the sale as the winner has 7 days after the GA ends to activate the game and mark it as received.

If you really want to make a giveaway by buying gifts from steam, I suggest you to make a region-restricted giveaways and refer to the price list in SteamDB.
Regional-pricing for the steam games in your country varies too much for each game. Sometimes it is 135% cheaper than US base price, sometimes it's just 5% cheap.
For some games you are only able to make giveaway for 45+ countries and for some other games you are able to make giveaway for just 7 countries.

The risk-free option is to make region-restricted GA just for your region i.e. Ukraine, but if you understand the pricing you can easily make GA for other countries too, if they fall under +10% price of the game.

Using the regional-restriction option when creating GA in steamgifts will filter out members that won't be able to accept steam gift from you. After the GA ends just add the winner in steam and send him the steam gift.

Here's an example that may help you if you want to add other countries too.

i'm afraid to even try to gift something from steam. i've seen deals before in the past that i would've liked to make a giveaway for, but as people have said, regional pricing can screw everything up. i'm in america and i'm pretty sure some regions vary drastically. knowing my luck, i'd make a giveaway and not be able to gift to the winner, then it's a whole debacle. i'd rather just gift keys.

Beside the region pricing troubles with gifting from steam that many already mentioned you can also run into other problems. If you gift too many games to different accounts or if you gift too many games in comparison to what you buy for yourself Valve thinks you're a trader and disables the ability to buy games as a gift. See e.g. Steam won't even let me gift games to my friend.