When I first went backpacking in the end of the millennium it was a completely foreign notion to me that I would be doing my laundry in a sink and to be fair at the start of it all I still didn't do my own laundry and thought it was really strange that people would do so.
Then things changed when I started moving from city to city and then started realizing that my clothes weren't really very dirty because i wasn't actually trekking, my clothes were simply sweaty and so I asked someone who was much more experienced than I was what the deal was here.
He told me something that all of you probably already know and that is that if you soak your sweaty clothes in a tub of water or a sink and then just squeeze them vigorously, rinse them, then hang them up to dry, that this is more than sufficient for t-shirts, vests, boardshorts, and other such common items that a backpacker is going to be wearing.
If you brought along dressy clothes I first have to wonder why it is that you brought that stuff with you and if you did you should probably pay someone to wash those for you.
Not all guesthouses are created the same so here are a few items that might help you to accomplish this task easily.
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Most rooms will provide some semblance of a drying rack (normally for towels) but not all do. In this instance a very cheap retractable clothesline comes in very handy. you can attach one end of it to something like say the curtain rod, and there is a hook on the other and that will attach to anything else in the room. In most countries, especially if you leave your fan on, you will be surprised how quickly a shirt or shorts can "air dry."
This came in really handy for me because after making mistakes and bringing way too many shirts with me on my first trip, I downsized and only brought 4 shirts with me in total. I would normally do some level of washing every day because if i was just washing a couple of things, it took no time at all.
Many people might simply say that they can just pay to have someone wash their clothes for very little money and in most cases they would be correct. However, if you are trying to keep the weight of your pack down (and I highly suggest you do) then there is a really good chance that you are not going to even have a couple of kg of laundry at one time. This means that your clothes will get mixed in with other people's clothes and these items are frequently lost.
As far as detergent is concerned, this can be problematic because generally speaking these containers are not resealable and opening up your backpack to discover that your detergent has exploded all over your stuff is not fun and is very difficult to wash out, particularly if it is liquid.
Therefore, getting a laundry bar is the best choice
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As an American, I regret to admit that until I started backpacking, this was yet another product that I didn't even know existed. You simply scrub some of it onto your wet clothes (paying extra attention to the pits!) and then suds it up in the water. It really takes almost no time at all.
If the idea of a bar of laundry soap doesn't appeal to you, then I highly suggest your transport the powdered or liquid detergent into a slightly more robust bottle that can seal - any old water bottle will do. These are far less likely to break open in transit and ruin your afternoon.
You can pick up one of those expandable clotheslines for just a couple dollars and washing powder and bars are available, as you would expect, around the world. There is no need to transport that sort of stuff on a plane and it is likely to be taken from you anyway... just get it at your destination. Believe it or nor, people all around the world wash their clothes.