Just follow Annie's questline until you get the option to buy the farm, then purchase the daycare upgrade for it :) You can see the next stage of her quest in her heart menu.
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You buy the farm the same way that you buy every other property - talk to Jessica in her office on weekday afternoons, ask to see the property listing, click on the property you want and then click "purchase".
If it's not showing up as purchasable then you need to talk to Annie after the event to make sure she's willing to sell.