How to buy a land and build a cottage in the United States?
There are many different rules in various areas of the US, but here are some broad guidelines.

Build

Just because some piece of land is in a residential area, it doesn't mean you can build on it. First you must determine zoning.  This is a categorization that a locality places on land, regulating what can be put on land (one family houses, multiple family houses, commerce, farm buildings, dockage, etc.). It also regulates how big a plot of land is needed of a given type of structure or usage (1/8 acre, 2 acre, etc.). Finally, you need to check if there are restrictions on the land, such as not subdivision, farm only, open land requirements. There are many pieces of land in residential areas that you cannot build a house upon.

Next you may need planning authority approval. This controls where on a piece of land you place a building, how a house is accessed from a road, whether accessory buildings are allowed and where they can be placed, where sewage disposal units or fields need to b e placed, whether fencing or foliage screening is required. Some juriosdictions handle this as a separate process and some relegate this to the building department.

Finally, you must comply with building regulations, if the area has them. At very least, most jurisdictions have health regulations covering drinking water and waste water. Most have building standards covering foundtion, construction, electricity, and plumbing. You may have to submit plans in advance for approval and may have to have various inspections done during or after construction to ensure compliance with rules and standards.  While there are national guideline standards that many jurisdictions adopt as regulation, there are a lot of local variations based on local conditions (such as climate) and practice.

Connect

Many areas of the US have utilities present on or at the edge of a given piece of property.  Many do not.  Vast areas have no central water or sewer service. If not, there may be an option (or a requirement) to hook into existing water and sewer. If so, you probably have to pay to run the lines to your property and then to any dwelling you build. There are often restrictions on how large a house you can connect.

If there is no central water and/or sewer available, you will have to install a well and a septic system.  Each locale has rules about the type and positioning of these units. These usually require installation by a licensed practioner, and a certification of compliance.

Electricity similarly is available in many locations at property lines, but if not, you may have to pay to bring power to the site. Some locations have natural gas hookups for heat, but again, if it is not already at the proerty line, you may have to pay to run a branch line to your site. Otherwise, oil, electric, bottled gas, wood may be needed for heat.

Address

Most locals have pre-assigned addresses for each parcel of land, generally referred to by the name of the access road and a number that may be arbitrary or based on a measurement from some reference point. If a piece of land is being subdivided, a new address may need to be generated by the local authority. These are often done on tax maps controlled by the town or county. 

In many areas, postal service is available to a mailbox at the roadside or to a front door (usually in city or dense suburban settings). Some areas have restrictions on mail boxes and do not allow street deliveries or require clustered boxes at the end of a road or other central location.  In many places, post office boxes (P.O. Boxes) located in a local post office are the more typical way of receiving mail.

As others have suggested, the range of issues may make it advisable to enlist the aid of a local builder to learn about and navigate the complexities of getting all the necessary pieces in place.