You start every life in town. The buildings you build and the upgrades you buy there are kept when you die. They also work right away, in the life you are playing.
Buildings go up to level 3. The first two levels cost gold, and the third also needs soul shards, which bosses drop. One life doesn't bring back enough gold to buy everything, so you build up the town over many lives.
The tavern
Your room is here, with your bed and your stash. Sleeping in the bed heals you. The innkeeper sells upgrades, such as a bigger stash, keeping items and more of your gold when you die, extra attribute and skill points, starting at a higher level, and better starting gear.
The merchant
The merchant sells potions and town portal scrolls, and buys your loot. He doesn't sell gear.
The builder
The builder puts up the other buildings and upgrades them.
The smith
The smith can enhance gear, upgrade a normal base to an exceptional or elite one, and reroll affixes.
The gambler
The gambler sells items you can't see before you buy them. You pick the kind of item, and the item you get can be any quality, up to unique.
The library
At the library you can unlearn your skills or your attributes and spend the points again. It also sells tomes, and blessings, which are buffs that last for one life.
The shrine
You give gold at the shrine for lasting boosts to life, damage and other stats. There is no limit to how many levels you can buy.