The beginning of the cleaning of clothing is the most important part of the entire process. This is the point where decisions must be made and materials gathered.

If you have a washer and dryer at home, you have an easier time of doing things. You do not have to worry about what other people may or may not do to your clothing. You can also do other things with the time your clothes are getting clean. Home is always more interesting than a stanger's laundromat.

If you must leave home, you have to consider how much change you are going to have to bring with you. You will likely need more than you think because laundromats, or perhaps your own landlord, are out to squeeze every last cent out of the desire to be clean. The cycles never seem long enough. Or maybe I just play really rough.

Both at home and at the laundromat, you really should buy your supplies somewhere else than a place which makes its money from laundry. I want you to save money. I hope you would want the same for me.
The materials that are unavoidably consumed in the process are water and detergent. The water line is already connected to a functional machine, but the detergent is up to the end-user to provide. Detergent comes in liquid and powder form. I usually go with powder because it is less expensive.
Optionally, fabric softener and bleach can be added to a wash. Personally, I like sheet fabric softener over liquid fabric softener because it is easier for me to remember to put it in this way. I have no rational reason for it being easier for me, but it is. I can not bear to forget the softener because I'm hooked on the soft feel that the fabric softener provides. I never, ever use bleach because I don't need my whites any more white. Thank you.

In any event, probably the most important thing to do is to seperate the shirts from each other by color. If you fail this step, you can end up with the proverbial pink shirt that used to be white because you threw a red shirt in the wash problem that seems to afflict everyone on American television.
There is a wide variety of thought on the optimal color segregation. Personally, I have so many whites that I almost always have to do a couple of washes of them alone no matter what. Likewise, if I do not have enough whites for this wash, I will have more later. White shirts are a unique color unto themselves that are almost always seperated from the other colors of clothing by all but the most lax color seperators. Beyond white, though, there are plenty of options. The lowest seperation method I would reccomend is lights and darks. The highest seperation method I would suggest is by individual color.

Growing up, I was taught to turn the shirts inside out so you could more easily clean the insides which tend to get dirtier. I do not know if this extra step really works as intended. I take the extra step because it is what feels natural, but you may or may not follow my path.

It is a good idea to carry your clothing in some sort of container. I use a pillowcase unless I have to also wash that case. In that case, I would possibly get a dedicated basket.

After all of that pre-thinking, you still have more thinking to do. First, you must judge how much clothing you are going to put in the machine. I'd shoot for 75% erroring on the side of less for maximum cleaning value. The mechanical process has a few variables that present themselves only at the individual washing machine. Namely, the position of the detergent dispenser and whether the interface of the machine is temprature, cycle, or based on both of those.
For the dispenser, if the dispenser is on top you can put the detergent in at any time before, after, or during the even loading of clothing and always before the water starts filling the machine. If the dispenser is not on top, you must put the detergent in while the water is filling up. This is fun to watch the first couple of times. For free shirts, you will want a half a provided cup, maybe, worth of detergent.
As far as the temprature or cycle setting, you will almost always want "warm" or "cold" as the temprature, and "permanent press" as the cycle. Some might feel that "hot" is good for whites, I find that for me it is not worth the chance of me being distracted to have whites with designs being washed in hot.

Note: I have heard about people putting their clothing and detergent in a waterproof container and going for a drive over rought terrain. I personally have not tried this method. The price of gas and the wear and tear and my car for a smaller amount of clothing being able to be washed per few hour trip would not save me any money.

If you are using liquid fabric softener, you would add it at the beginning of the wash.

If you are using sheet fabric softener, you would throw it in at the beginning of the dry.

Even before the fabric softener, though, you really should feel around for the lint screen. Yank it out, take out the lint that has accumulated, and go back to town for a dry night out.

After that, about every free shirt I run into wants to be dryed on a low setting. New free shirts in particular should be given a low treatment since they are more likely to shrink. Some shirts want medium heat, and that is good too. I would avoid hot, even for whites.

An alternative to using a dryer is hanging your free shirts on a line attached between poles outside. This method is very cost-effective, but costs in time and is weather-dependent.

NO! I will not ruin the designs on my free shirts by ironing them. That and the fact that non-decorated shirts also do not need to be ironed. This will not change until I get free dress shirts, but cotton/polyester t-shirts are almost completely the shirts that end up being free.

"Ironing" itself involves stretching out on a pleasure board and applying a whole lot of heat in a circular motion.

For t-shirts, either folding or hanging works. The preference is yours to develop. Since I do not have anywhere near enough drawer space, I hang all of my free shirts.

To fold something, you put one part of the garment over the other part. This process often produces symmetry and almost always reduces space.

Hanging often involves putting one's neck in a noose, but it certainly does not have to be that way! For most people, getting a plastic or metal triangle with a hook at the top provides and excellent way to hold a free shirt in position.