Keeping clothes clean without access to a private washer and dryer can be expensive and time consuming. Also, the man does not like you showing up around his customers with clothes smelling like yesterday's body odor unless you work some outside job. No one is going to tell you you smell either. It can affect peoples attitudes significantly.
If you are between housing, Low Impact Crashing has creative ideas as well.
It is very possible to find a apartment complex with or without a gate or locked laundry room. Larger complexes are best to check. Go at night when landlords or nosy staff are away if you do not live there. Expect to extorted by the landlord if those apartments have no washer connections in the units and he has a monopoly. Many landlords charge outrageous prices for old, poorly working machines.
Bring stir sticks, cue tips, or zap strap for coin operated machines. Push the coin mechanism in, remove it a quarter inch, and insert these items as wedges about 45 degrees in angle. Force the slot in, and the machine should start.
Please note that some machines have a "coin gate" that will shut when you push in the coin mechanism, screwing up your picks and not allowing the machine to start. Also realize that this is technically a criminal offense, and if caught you may be charged with theft of services or mischief.
If you live near a college campus with dorms, they often have free (or cheap) laundry machines. Go to the nearest campus, wait by the door with your laundry, get let in by some sorority type, and make your way down to the laundry room. They tend to be placed in the basements of residence halls. Students often leave detergent around, so cop some of that, and you're golden. See also Low Impact Crashing for more ideas. Be careful as more campuses are requiring school name badges to be worn at all times. Be sure you look like a student.
If you have inside information and are feeling crazy, some larger companies will have laundry rooms for their employees. At many these are free. You can wander around campus and just ask "Hi, I'm new here ... oh, I forgot my badge." Corporate rent-a-pigs assume you are a lost client and will usually gently escort from the premises at worse, unless they think you stole something. Companies are like cults or tribes, they often have their own specialized lingo. Be sure you look like you(and your container for laundry) belong there.
A problem is many places have RFID and keypad door locks. You really can't get too far without a badge or a code. Some places like casinos or hotels have staff that washes and presses the clothes for folks and will recognize you.
Some companies may have do it yourself guest registration; if you snag a registration badge and step out of the lobby security will mistaken you as "lost" and often ignore you.
Infiltrating has more information if schemes like this tweak your interest.
Of course, you can always work for a place that has this as an employee benefit. However, we have found most of the places that offer this tend to be in hospitality type fields like extremely large destination resort hotels or casinos and will only wash work related clothes under threat of disciplinary action. Of course, the boss man is immune to this rule. Still, not having to worry with scrambling to get clean wage slave outfits with limited time to get to work can be a good thing.
If you at least have detergent, hot running water, and a bathtub, you can wash clothes old school style. It is very labor intensive and does not take care of pet hair or some tough stains quite as well. Be sure to rinse the detergent out thoroughly as it can cause skin irritation. Cheap powder detergent can also leave residue on the clothes if not rinsed off very well. In general, use very little detergent because agitation of the clothes will do most of the work of removing dirt and grime. Be careful over soaking travel soiled white socks in bleach as it tears them apart.
Hanging dry may keep wrinkles down for most normal use. You will still need an iron for occasions where you must be clean pressed like waiter uniforms or business attire.
Quick drying can be done by placing a garment flat between two towels, and you will have to press on the sandwich to squeeze out the water so the towels absorb it. After doing this several times, the garment should only be a bit moist so the rest of the drying can be done by placing the garment near a heat source. Only do this if you have no other option and need a clean shirt quick.
If you know someone that has a washer who will not steal any valuable clothes you may have, you could make a deal to buy detergent, a pack of smokes, favor, or whatever for use. Some may not be agreeable to this, since they may not expect company for 2 hours every few days and it can get old.
In Amerika people usually machine wash their still clean clothing after wearing it for only a few hours, this is ridiculous especially in cooler or dryer climates where for most people socially unacceptable body odors are not produced in large amounts to linger in the garments. If the clothing you are wearing is not actually dirty or just has a few food spots you can often just spot wash the dirty bits if required. You may still have the funk smell, but even in winter a few hours of air and sunshine will often get the body stink out, rain is not a problem either as long as the wind doesn't blow your garments into a mud puddle, just let it drip dry after the rain shower. This method is much easier on your clothing than machine washing and will lead to much longer life especially for natural fabrics.v Synthetics and some colors are best hung in a well vented area indoors or in the shade to prevent sunlight degradation of the fibers and some dyes and pigments. The smell test will sometimes fail clothing after a few airing outs and you will need to use soap or detergent in a more conventional wash. Your underwear and socks which end up collecting most of the body odor are easily washed in a small container and hung to dry with your outer clothing.
Even if washing or hanging outside is not an option hanging your already worn clothing open over a chair or door as you sleep will let some of the smell dissipate and is quite a bit better than wadding your garments into a ball and throwing it onto the ground where the stank will just get a stale tinge.
This may not work but can be worth a try in public laundries. Wait in a laundromat. Tell someone with a light load that you will watch the machine for them if you can stick a small amount of your clothes in with theirs.
Homeless Shelters and Drop In Centers.
Many cities have laundry services for the indigent. Sometimes this is part of a shelter's service and other times a separate facility. You usually have to sign up and pick up your clothes at a later time. Most will not let you wash them yourself for fear you may "break" something. Some charge very small fees while others are free. They will probably not wash weeks of laundry, either, and probably will set a hard limit of maybe 2 to 5 outfits. Of course, like any "charity", expect strict restrictions, rules, maybe some snide remarks,and regulations to be able to use this service. Some places even operate on a lottery system or only serve the first few people that show up, so it is very possible that you could be carting all your smelly clothes over there and be out of luck. Only use this as a last resort.
Creek, Stream, and Ocean Washing
It is possible to wash in a creek, lake, or stream. The only problem is that many bodies of water like this are highly polluted with oil, pesticides, and other nastiness and have a high degree of sediment in the water. This includes almost all creeks running through major cities, near river ports, and heavy agricultural areas. It still may knock off some stench if it is not too polluted, though. So, in this case, whites and professional type stuff are out of the question as some creeks and lakes will ruin those clothes. A clear stream like those in the Appalachians or Rockies would work much better.
Be sure to let the clothes dry after dipping them in the lake or creek, especially if you have open cuts or sores, as these bodies of water carry bacteria.
The ocean can be an idea as well. However, your results can vary with this. Some beaches like those in Florida are crystal blue in places. Others, like the Mississippi Gulf Coast is nastier than most reservoir lake water.
Now, in the old days of our great, great grandparents and even in third world countries, this is still a viable way. If you are dealing with caked on mud or dirt, get an old school wash board and start scrubbing. Some of our ancestors would fill a wash tub full of creek water and heat it over a fire to help remove the tougher dirt. Of course, this was an all day event and took the whole family.