Maybe I am late to the party, but one thing to mention is that you can get free loaner gauges and a loaner vacuum pump from autozone. I used these to recharge two pickup trucks after having to replace components inside the cabin HVAC boxes. I replaced the blend door actuator on my 07 Ram 1500 Laramie, and then my son's Nissan Frontier's heater core went. I also helped my son-in-law recharge his Chrysler Pacifica mini-van with the 1234yf refrigerant. He hit a critter on his way to work and in a once-in-a-thousand chance, the critter was thrown into his condenser and put a hole in it. Never have seen anything like it. Repair shops wanted very large dollars to fix. I showed him how to do it for about $250, half of which was the refrigerant price gouging.
Now, it is more than possible to charge or recharge your system yourself if you do the required research, make sure you understand how to work the gauges, and also understand the fundamentals of how the AC system works.
Somewhat simplistically, a fully charged AC system with engine off starts out with both the high and low sides at comparable pressures since the compressor is not compressing anything. Then on a warm day, when the engine starts and let's say Max AC is engaged, the system begins to cycle: the low side is compressed to the high side which then decompresses to the low side, to create cold in the evaporator chamber in the cabin HVAC box behind the dash. Pressure sensors placed at various locations along the refrigerant path react to pressure changes to determine whether to keep the compressor on or turn it off. If the pressure goes too low on the low side, or too high on the high side, the compressor is turned off. Turning off the compressor will then cause the two sides to start to equalize in pressure. When the pressure is high enough on the low side and low enough on the high side, the compressor will be turned on again and the cycle repeats. There are other conditions being monitored as well that control the clutch, the electric fan, etc. For example, the cabin temp is monitored to see if the compressor is no longer needed as the desired temp has been reached. Or, the electric fan may be turned on if it is needed to assure airflow across the condenser. Typically, if Max AC is selected the fan will be on by default. Bottom line, if everything is working the way it should, then the basic operation is a cycling between low and high pressure limits of the refrigerant balanced against temperature readings in the cabin.
You also need to know the specs for your car's system which are usually found on a sticker under the hood or in the engine bay somewhere. This sticker will tell you the oil and refrigerant capacities of the system and also the type of oil and the type of refrigerant the system uses. You MUST use the correct oil and refrigerant type for your system. You must never overfill either the refrigerant or the oil. Better to run a bit low on either, but not too low. If you are replacing components of the AC system, then you typically must add some oil since the oil circulates with the refrigerant. So, you may need to add oil if you lose an AC component. For example, in the case of the Chrysler, we were replacing the condenser obviously, and also the receiver/accumulator/dryer. [Anytime you discharge a system completely it makes good sense to replace the receiver/accumulator/dryer which is usually very inexpensive.] You can find help on how much oil to add per component online, but it will usually be 1-3 ounces as I recall depending on what is being replaced. I think we added 2 or 3 ounces to the Pacifica, for example.
The 134A systems and 1234yf systems have different connector interfaces and different refrigerant can characteristics. They use different gauges becuase of this and have different pressure scales as I recall. Others please correct me, but I think I recall that the 1234yf cans screw in counterclockwise vs clockwise for the 134A cans. So, be careful about the details. Think deliberately and talk yourself through each step and have someone with you to verify what you think you did and why.
For example, NEVER open the high side gauges when adding refrigerant, just the low side blue ones. Only open those red high side gauges when vacuuming the system. When adding refrigerant, you only need the red hose to connect so you can read the high side pressure. You don't want to do anything to the high side at this point going forward except read the pressure on that side.
So, with this in mind, you can troubleshoot some obvious problems pretty easily. For example, you watch the compressor when the engine is on and MAX AC is selected. The compressor clutch keeps cycling on and off every 3 seconds or so. Well, this often means the pressure sensors are reading too low on the low side every 3 secs and shutting down the compressor. Then pressure builds on the low side as the pressures on both sides equalize, and it turns on again only to fall quickly and repeat. Possible problem is not enough refrigerant. You might add a bit (say 2 ounces) and see what happens. Often after adding a few ounces, the compressor stays on longer and then you just need to figure out how much more to add to get the system stable and cycling in response to cabin temp, not low refrigerant pressures. That is where the gauges can help. You should be able to find for your vehicle the desired working pressures on the low and high sides for a given ambient temperature and target those pressures as you add refrigerant. Then you'll find the vents blowing cool air and your AC is back in business.
Again, my disclaimer is that this all too brief explanation is general and does not nearly cover all the other aspects of the system that might need troubleshooting. But I have found that most of the time, the system has integrity and troubleshooting can be done around that hypothesis in an attempt to falsify it. Areas not covered that are also common include a leaky system that causes the low refrigerant condition in the first place, a bad clutch coil that will not enage the compressor so you can further troubleshoot the system, a faulty pressure sensor that could be causing your system to malfunction in a way that could fool you into thinking it is low on refrigerant, and a faulty fan or fan control that prevents air circulation across the condenser. These and many others are all possible, but less likely conditions. So, I tend to start with the most common and work down the list. Gauges help you avoid wrong guesses and unproductive troubleshooting if you can get comfortable reading them and watching the system behave through them. And you can simply borrow a set and watch the system operate without affecting it at all. This would be the "read-only" state available with gauges. Keep the valves closed on the gauges and just hook up to the low and high side ports. Doing that alone is a huge step forward for the newbie and can get you comfortable with where the connection ports are, how to hook up the hoses, what to look at on the gauges, and what it all means.
But IMHO the vast majority of issues are associated with getting the system filled and lubricated properly. There are many mistakes that you can make, as with all DIY repair. I have made many and will continue to do so. But I am hoping this brief overview will be of some help as you deal with the problem yourself or enlist a repar shop to help.
I also invite others to correct any errors I may have made in my descriptions. I welcome criticism leading to refinement of my understanding as well.