We can't give you a simple answer because there is no "Standard" way for case fans to be connected. However, there ARE "standard" fan wiring types, and "standard" ways to supply power to them. If you learn the terms, you'll know what to look for in spec sheets.
There are several fan common SIZES - 80mm, 100mm, 120mm, 140mm, and a few others. They all have square shapes and the size denotes the side of the square. Generally, of course, larger fans move more air. All fans should have moulded into their plastic cases two arrows. One goes around the case to show you "normal" rotation direction (that is, when connected to DC power with the correct polarity); the other point in the direction of air flow through the fan. Almost all are made somewhat symmetrical so that you can fasten them to (whatever) pointing in either direction, according to your needs. Hopefully they will come with screws to fasten them. Some come with rubber washers on the mounting holes to reduce transmission of fan vibration to the case.
WIRING generally falls into one of three groups, noted by the number of wires going into the fan motor. ALL run on 12 VDC for full speed, and all CAN run slower a reduced voltage.
Basic or 2-pin fans have only 2 wires entering the motor - usually Red for the +12 VDC supply and Black for the Ground lead. Most often these are fitted on the end of the wires with what is called a 4-pin Molex male connector. It has 4 round pins in a straight line, and is about ¾" wide. This is the type used to power older IDE hard drives and optical drives, and it mates with a female connector on wires coming directly from the PSU. The supply connector has 4 wires to it, but the fan only uses 2 of them. This fan type can only run at constant full speed if connected that way. This fan type also may be used with third-party fan controller modules that draw their power from the PSU in the same way, but then reduce it before sending it out on a new connector to the 2-pin fan that runs slower according to how you set the fan controller.
3-pin fans have been very popular for some time now. They use a smaller female connector with three holes in a straight line to mate with a male port on a mobo. The mechanical details of the plug and port connectors ensure that they only go together one way to keep connections correct. Three wires go to the fan motor - Black for Ground, Red for +VDC supply, and Yellow for a new speed signal. I said "+VDC" because the way the mobo can control fan speed is to vary this voltage supply from 0 to 12 VDC - it is not fixed. The speed signal is a series of pulses generated inside the motor (2 pulses per revolution) that are sent back to the mobo on the yellow line. The mobo circuits then can measure fan motor speed and check whether it is turning at all. It is possible to plug such fans into other places, like into third-party controllers or direct to a PSU Molex output via an adapter, but then the speed signal will never get to the mobo to be monitored.
4-pin fans are an advancement over 3-pin ones. They have a similar female connector designed so that they can be plugged into EITHER a 3-pin or a 4-pin mobo male port connector to help with backwards compatibility. The lines here have different colours from the 3-pin ones, but the first three wires have the same function: Ground, +12 VDC, and Speed Pulse signal return. The last wire is a new PWM signal which looks a bit like a square wave, except that it is not 50% on and 50% off. Its % ON varies to vary the fan speed. 4-pin fan motors have inside them a tiny controller chip. It takes the +12 VDC supply and modulates it using the PWM signal, thus controlling how much of the time the motor actually has current flowing through it, and thus controlling the speed. For backwards compatibility, the PWM signal acts like an inhibitor - when it is "on", the current flow through the motor is cut off, and vice versa. Hence if you plug a 4-pin fan into a 3-pin port the fan will not receive any PWM signal and the full voltage on the VDC line will always be fed to the motor. But the 3-pin port is adjusting that voltage to achieve fan speed control, so the 4-pin fan still can be controlled by a 3-pin port.
On the other hand, if you plug a 3-pin fan into a 4-pin port, the 3-pin fan connector does not send the PWM signal to the motor which can't use it, anyway. However, the 4-pin port does not vary the +12VDC supply line the way a 3-pin port does, so a fan connected this way will always run at full speed.
Mobos these days come with both 3-pin and 4-pin fan ports on them in an inconsistent mix of which serves what. 3-pin ports can only function in their original design manner, but the design of 4-pin fans means that they CAN be plugged into 3-pin ports and work just fine. Doing it the other way could have various results. If the 4-pin fan port only acts according to the 4-pin design, a 3-pin fan plugged into it will always run at full speed - no control. But some 4-pin ports allow you in BIOS to set them to change and behave as 3-pin ports, achieving control. In fact, some mobos are smart enough to detect this situation on their own and automatically change a 4-pin port into a 3-pin port when it is connected to a 3-pin fan.
Power Sources and Control
Power is available from a 4-pin Molex output connector from the PSU, and usually one uses its +12VDC and Ground leads for this so the fan runs full speed. This allows no speed control, and sends no fan speed signal to the mobo.
You can buy and install third-party fan speed controllers that allow you to manually set the voltage going out to the fans it controls, thus achieving speed control, but not automatic. Some of these controllers allow you to connect 3-pin fans to them so the fan's speed signal is sent to the controller to be displayed for you, although that speed is not sent to the mobo. A few also provide extra temperature sensors you can stick into place inside your case, but these are not the same as what the mobo provides (see below).
Motherboards now all have some fan ports on them that provide power to the fans, control their speed, and monitor of their speed. NOTE that the mobo can tell you a fan's speed, but it does not need or use that signal to actually do the control.
You will find three types of mobo fan ports. There is always a CPU_FAN port for the CPU chip cooler system. It carefully monitors its fan's speed for safety - if it senses that the fan is not turning, it often immediately sends out an alarm and shuts down your system to protect the CPU for overheating, even without waiting for the overheated situation to develop. For this reason, if you opt NOT to power the CPU cooler from this port and thus will not provide that fan's speed signal to the mobo, you may have to go into the CPU cooling system setup in BIOS and tell it to ignore the non-existent fan. But if you do connect your CPU cooler here and allow it to control automatically, here's how it works. Every CPU has its own temperature sensor built in, and its signal is available on one of the chip's pins to the mobo. The mobo uses that measured actual temperature inside the CPU, compares it to the temperature target set for that CPU type, and adjusts the fan speed to keep it at the right temperature.
Many mobos have a port labelled PWR_FAN that looks like a common 3-pin port. Some PSU's have a set of wires coming out of them with an apparent female 3-pin fan connector on the end. The intent is that you connect these together and the PSU's internal fan will send out its speed signal to the mobo via this port so the mobo can measure and display it, and monitor that fan for failure. The mobo does NOT control the fan inside the PSU. That PSU fan MAY change its speed because the PSU itself controls its own fan, but the mobo is not doing that function. If you do not have such a set of wires coming out of your PSU, the intent is that you do not use that mobo port. BUT many mobos provide the +12VDC and Ground signals on the port, so you can connect a standard 3-pin or 4-pin fan to it, and that fan will run at full speed always.
The mobo will have one or more SYS_FANn ports for case fans. These may be either 3-pin or 4-pin. The mobo has its own temperature sensor built in somewhere (maker's choice about what is most important to monitor) and it uses that signal to control the speeds of the fans connected to the SYS_FAN port(s). The details are a bit confusing sometimes. For example, I believe on my mobo the SYS_FAN1 port is automatically controlled this way, but the SYS_FAN2 port has no automatic control - it just runs full speed.
It is always a good idea to connect the "correct" type of fan to a port - Match 3-pin to 3-pin, and 4-pin to 4-pin. I believe it is always a good idea to have the CPU fan connected to the mobo's CPU_FAN port, and to have it automatically control that fan.
A dilemma some people run into from time to time is there are not enough fan ports on the mobo for all the case fans they want (or even for 2 CPU cooling fans). For this you can get adapters that allow you to connect 2 fans to one port. My rule of thumb is that most mobo ports can power up to 2 fans, but not more. The limit is in start-up current, which is much higher than continuous running. If that is still not enough, you will need to power some fans directly from the PSU via a 4-pin Molex output. Those outputs can supply much more power that a mobo port, and several fans can be run from one PSU output via adapters - just without any speed control or fan speed monitoring.