If you want to trade Pokémon, choose “Link Trade” from the menu. You’ll be brought to your Pokémon Box, where you can select one Pokémon to trade. Meanwhile, you can see what Pokémon your partner has currently selected near the top. Once you’ve decided, select “Offer as a trade”.
In the next screen, you can confirm the trade by selecting “Trade Pokémon”, check your partner’s offer by selecting “Check offered Pokémon” and so forth. Note that these options will only appear once your partner has selected a Pokémon to trade; otherwise they’re greyed out.