Watching my old roomies washing dishes has been..illuminating. They do a lot of Bad Things when it comes to washing dishes, and I guess if I'm going to get you better at washing dishes I should sort of show you why they are Bad Things.
Not keeping an open sink: If possible, you want an open sink and if possible the one with the garbage disposal. Having an open sink when it comes to food prep is a great thing as it gives you an open space to wash whatever you are cooking as well as the ability to drain off liquids and fat as possible. If you pick the wrong sink, it means you need to move all of those dirty dishes out of the way in order to use the garbage disposal.
Don't bleach plastic cutting boards: It may sound good, as bleach utterly destroys germs, but bleach is hard to rinse off and if it's not completely removed it can cause you to get sick (as with soap, we're talking mostly nausea and possible vomiting, so it's not usually dangerous, just inconvenient). It also causes the boards to break down faster, giving germs a lot more places to hide later on. [I prefer to use wooden boards anyway...]
Don't soak plates and silverware: If they need it fine, but in general avoid it. The big issue here is that the soap has a chance to coat the dish, making it harder to wash off and possibly causing you to be sick. Also, you're creating a nasty mix: You have a pool of water with a lot of food particles that can feed bacteria. Any bacteria that penetrates the soapy layer, and keep in mind that soap in and of itself doesn't kill germs, has a great place to breed. So if you soak plates and silverware without need, you're adding soap and bacteria to your dishes. It also wastes time and water.
Don't use cold water: Soap works best against lipids, making it highly effective against fats and grease, but not so much against germs; it weakens them somewhat, so it takes hot water to actually kill them. Admittedly it doesn't need to be boiling, but using the hottest water you can works for most germs. Soap plus hot water is an even better mix; if you miss something you at least know it was sterilized. Also, hot water will rinse off any soap from the dishes (meaning you soak your dishes if you like, I'm just suggesting you don't).
Don't wash pots and pans separately: While it makes a certain degree of sense, there is no reason to do so unless you're doing a large amount of dishes; too many people get fixated on how well organized dishes look on the packages and figure that's the way you need to do it. In reality, you can actually stack them pretty high. Doing them with the other dishes also saves on water and soap.
Don't use a towel to dry dishes: A towel will get damp after even a few dishes, allowing it to spread bacteria. Air drying is actually better, and if you used hot water the dishes should dry quickly.
Don't worry about a greasy patina on pots and pans: Pots and pans tend to pick up whatever is cooked in them and this applies doubly to fats and grease. This means that over time your pots and pans, especially those used for frying, will tend to pick up a slightly greasy look. All it means is that the pan is well seasoned, and not necessarily dirty.
Dishes should not be a major stress issue. Just do them, get them over with, and go on to whatever else you want to do. It's definitely a part of cooking, and something you need to do well, but some people stress over them just too much. Just relax and do them it's not rocket science....
Not keeping an open sink: If possible, you want an open sink and if possible the one with the garbage disposal. Having an open sink when it comes to food prep is a great thing as it gives you an open space to wash whatever you are cooking as well as the ability to drain off liquids and fat as possible. If you pick the wrong sink, it means you need to move all of those dirty dishes out of the way in order to use the garbage disposal.
Don't bleach plastic cutting boards: It may sound good, as bleach utterly destroys germs, but bleach is hard to rinse off and if it's not completely removed it can cause you to get sick (as with soap, we're talking mostly nausea and possible vomiting, so it's not usually dangerous, just inconvenient). It also causes the boards to break down faster, giving germs a lot more places to hide later on. [I prefer to use wooden boards anyway...]
Don't soak plates and silverware: If they need it fine, but in general avoid it. The big issue here is that the soap has a chance to coat the dish, making it harder to wash off and possibly causing you to be sick. Also, you're creating a nasty mix: You have a pool of water with a lot of food particles that can feed bacteria. Any bacteria that penetrates the soapy layer, and keep in mind that soap in and of itself doesn't kill germs, has a great place to breed. So if you soak plates and silverware without need, you're adding soap and bacteria to your dishes. It also wastes time and water.
Don't use cold water: Soap works best against lipids, making it highly effective against fats and grease, but not so much against germs; it weakens them somewhat, so it takes hot water to actually kill them. Admittedly it doesn't need to be boiling, but using the hottest water you can works for most germs. Soap plus hot water is an even better mix; if you miss something you at least know it was sterilized. Also, hot water will rinse off any soap from the dishes (meaning you soak your dishes if you like, I'm just suggesting you don't).
Don't wash pots and pans separately: While it makes a certain degree of sense, there is no reason to do so unless you're doing a large amount of dishes; too many people get fixated on how well organized dishes look on the packages and figure that's the way you need to do it. In reality, you can actually stack them pretty high. Doing them with the other dishes also saves on water and soap.
Don't use a towel to dry dishes: A towel will get damp after even a few dishes, allowing it to spread bacteria. Air drying is actually better, and if you used hot water the dishes should dry quickly.
Don't worry about a greasy patina on pots and pans: Pots and pans tend to pick up whatever is cooked in them and this applies doubly to fats and grease. This means that over time your pots and pans, especially those used for frying, will tend to pick up a slightly greasy look. All it means is that the pan is well seasoned, and not necessarily dirty.
Dishes should not be a major stress issue. Just do them, get them over with, and go on to whatever else you want to do. It's definitely a part of cooking, and something you need to do well, but some people stress over them just too much. Just relax and do them it's not rocket science....