You can expand your village by clicking unclaimed land adjacent to your village. As of a recent update, there is now a confirmation popup, which asks you whether you really want to purchase the land expansion. But make the choice wisely! There is still no way to undo a land expansion.
Your first ice world expansion is free, as part of a tutorial. For the rest you will need to pay a certain amount of either Coins or Acorns. The coin cost increases exponentially (more & more rapidly) after the first 10 blocks while the acorn cost increases linearly (proportionally). However, keep in mind that coins have fewer uses than acorns and are the resource that is easier to acquire. Eventually as you level up, you will continue to accumulate coins but have fewer things to spend them on, while there is almost always something left for you to buy with acorns, especially limited items that could come out at any time. So don't waste your acorns on land expansions! See the Earning Coins page for all the ways to earn coins.
When expanding, look for Decorations on the land - you'll get them for free by expanding there.