Using the Downtime rules
You come to your GM and say "I want to buy an inn", then the GM checks the average cost of an inn (about 2,130 gp) using the Downtime rules. If there's one available, you negotiate the value with an NPC and the inn is now yours. If none is available, you can build your own (see Gaining Capital and Construct Buildings). Building your own inn will cost half the price, but will take much longer to get it done.
This is a sample inn:
Create 52 Goods, 5 Influence, 47 Labor (2,130 gp)
Rooms 1 Bar, 1 Bath, 1 Bedroom, 1 Common Room, 1 Kitchen, 1 Lavatory, 1 Lodging, 1 Stall, 1 Storefront
A place for visitors to stay and rest.
Of course, you and your GM could always customize this. The inn may have more rooms, a shrine, or even two bars, you just keep adding (or removing) rooms and adjusting the price accordingly.
Finally, it is time to run your business. The book did a terrible job at proving the total earnings of those sample buildings, so you have to sum up the earnings of all rooms and figure out the total yourself. Regardless, all business assumes you have at minimum a group of unskilled workers so you can run the business without issues while supervising them. So, you don't have to worry about hiring bartenders and maids for your inn.
This will allow you to make all those income checks mentioned in the rules, as long as you don't stay away from your business for more than a week. If you pretend to go adventuring and has no idea when you will come back, hire a manager. They will eat up most of your earnings (if any), but will reduce the risk of you losing the business to random events, bandits or even politicians (look up Capital Attrition on the Upkeep Phase). An Innkeeper for instance will cost you 2 gp a day.
Wage 2 gp/day
Skills Appraise, Diplomacy, Knowledge (local), Profession (any one)
An Innkeeper runs an establishment focused on hospitality. He’s typically a 3rd-level commoner or expert, but could also be a retired fighter, rogue, or warrior. An Innkeeper sees to the day-to-day operation of an Inn, Tavern, hotel, restaurant, or exclusive private social club.
Finally, you may also hire a team of workers to run your business, called Teams. Each team is a group of a couple of skilled (or unskilled) individuals that will increase your earnings on any building they are working on. A group of laborers for instance, could perfectly run an inn for you and grant you an additional +2 on your Capital check. But they have an initial cost of 70 gp, or 1 Influence and 2 Labor capitals, which is very costly for the little profit they will get you.
Earnings gp or Labor +2
Create 1 Influence, 2 Labor (70 gp); Time 0 days; Size 5 people
Upgrades To Drivers, Guards, Lackeys, Sailors, Scofflaws
At the end of each Downtime Phase (a day), you can run your Capital check to see how much you earned that day. To make things simpler, in my tables, I note down the date the player lastly had a downtime event, and we make all those checks when they return, or take-10 on all of them and see the result.
The rules are described under Income Phase. You Determine Building Income by making a Capital check. You do this by picking a type of capital you want to earn (gp, Labor, Goods, Influence, or Magic) and make a check for every organization and business you own. An inn would be a single check with the sum of all capital bonuses for that type.
Running a business while adventuring
As described under the Upkeep Phase, you need to visit or contact (or hire a manager) your business regularly, or you risk losing it. After 7 days with no word from you (the owner), you start to take Attrition (you lose 1 of each capital type), and after 30 days, you risk losing it. When you finally return, you have to make a Leadership test (1d20+level+charisma, see the Leadership feat) against a DC equal to the number of days away. Failure means your business is gone and you will not earn anything from it, as the Upkeep is the first phase during Downtime.
Because adventuring is dangerous work, if you’re away from a settlement for 30 days or more, you risk losing control of your businesses there as employees begin to wonder whether you’re dead. Upon your return, you must attempt a leadership check (1d20 + your Leadership score) against a DC equal to the number of days since you last had contact with that businesses – 10 (so if you’ve been gone for 30 days, the DC is 20). Having contact with the business requires visiting it personally, sending a qualified representative on your behalf (such as a cohort or manager), or sending a formal letter or magical communication (such as dream, sending, or whispering wind); doing so resets your number of days away to 0.