• Any extra water can be used for flushing, but you should use the "dirtiest" water for this first since it is the last use that water will have. If you're storing the water in a bucket, you can just dump a gallon right into the bowl to flush.
• If you grab the soapy water from the washing machine, you can use it for washing dirty stuff -- scrubbing the toilet bowl, cleaning out trash cans, etc.
• The cleaner water can be used for watering plants. Be careful about what you use for cleaning products, and you can probably use the water on more of your plants. Be careful about what water you use on plants that you're eating directly -- I don't think I'd use bath water on my spinach, for example.
• If you have a top-load washing machine, you could pour in some of your cleaner water into the initial rinse water.
• If you want to all-out, you can build a slow sand filter -- even if you don't get the water back to fully potable, you can at least move it back up the cascade a stage or two. E.g. perhaps the washing machine outflow can be reused, assuming you can dump into a top-loader.

A note of caution from "The Permaculture Handbook" (Peter Bane), p. 170:

Greywater should not be exposed to human contact more than 12 hours after initial use. [...] greywater that is not being actively purified by plants, animals, and soil microbes will culture pathogenic microbes quickly, becoming black water

In an apartment, you don't have a yard, trees, etc to dispose of greywater immediately and might be tempted to store it for a period of time. Keep the warning above in mind, and make use of your greywater appropriately. A bit of planning in timing your water-generating and water-using activities might be helpful. (E.g. do laundry when you need to water plants.)

• Any extra water can be used for flushing, but you should use the "dirtiest" water for this first since it is the last use that water will have. If you're storing the water in a bucket, you can just dump a gallon right into the bowl to flush.
• If you grab the soapy water from the washing machine, you can use it for washing dirty stuff -- scrubbing the toilet bowl, cleaning out trash cans, etc.
• The cleaner water can be used for watering plants. Be careful about what you use for cleaning products, and you can probably use the water on more of your plants. Be careful about what water you use on plants that you're eating directly -- I don't think I'd use bath water on my spinach, for example.
• If you have a top-load washing machine, you could pour in some of your cleaner water into the initial rinse water.
• If you want to all-out, you can build a slow sand filter -- even if you don't get the water back to fully potable, you can at least move it back up the cascade a stage or two, and/or allow it to be safely stored for longer periods. E.g. perhaps the washing machine outflow can be reused, assuming you can dump into a top-loader.

Sources

• Dish water is controversial as a source of greywater -- I often see it categorized as blackwater. If you do your dishes by hand in a tub.
• If you have a washing machine in your apartment, it should be easy to reconnect the outflow hose to a bucket. Just make sure (a) the bucket is big enough and (b) the hose is securely attached so that you don't make a mess! (Again, hopefully it's obvious, but if you're washing baby diapers then this is blackwater -- don't keep it hanging around, flush it away.)
• If the drain pipes connected to your sinks are accessible, they are usually easy to disassemble (either unscrew or slide the pipes apart). You can put a bucket underneath, just be careful that it doesn't overflow. (The same note re: blackwater applies here if you're doing dishes by hand, or if you manage to disconnect the kitchen sink below a dishwasher outlet.)
• If you can't get to the sink pipes, consider placing a bowl in the sink to catch water when you wash your hands.
• Similarly, men can shave with a bit of water in a bowl instead of letting the water go down the drain.
• I think taking a bath is probably a bigger water waster than taking a quick shower, so I don't think it's worth switching to baths just so you can reuse the water, but if you do take baths, you can scoop out most of the water with a pail before opening the drain. (You'll either need someplace to store it, or you'll have to be able to use it right away though. And if you have little ones in the house, don't keep a tub full of bath water hanging around!)

Uses

• Any extra water can be used for flushing, but you should use the "dirtiest" water for this first since it is the last use that water will have. If you're storing the water in a bucket, you can just dump a gallon right into the bowl to flush.
• If you grab the soapy water from the washing machine, you can use it for washing dirty stuff -- scrubbing the toilet bowl, cleaning out trash cans, etc.
• The cleaner water can be used for watering plants. Be careful about what you use for cleaning products, and you can probably use the water on more of your plants. Be careful about what water you use on plants that you're eating directly -- I don't think I'd use bath water on my spinach, for example.
• If you have a top-load washing machine, you could pour in some of your cleaner water into the initial rinse water.
• If you want to all-out, you can build a slow sand filter -- even if you don't get the water back to fully potable, you can at least move it back up the cascade a stage or two. E.g. perhaps the washing machine outflow can be reused, assuming you can dump into a top-loader.

Sources

• Dish water is controversial as a source of greywater -- I often see it categorized as blackwater. If you do your dishes by hand in a tub, then you don't have to worry about modifying any plumbing. Dish water may be categorized as blackwater because it will often contain grease, fat/oil, and food particles and you (a) don't really want to dump this on plants -- especially houseplants -- or (b) want to keep it hanging around for very long.
• If you have a washing machine in your apartment, it should be easy to reconnect the outflow hose to a bucket. Just make sure (a) the bucket is big enough and (b) the hose is securely attached so that you don't make a mess! (Again, hopefully it's obvious, but if you're washing baby diapers then this is blackwater -- don't keep it hanging around, flush it away.)
• If the drain pipes connected to your sinks are accessible, they are usually easy to disassemble (either unscrew or slide the pipes apart). You can put a bucket underneath, just be careful that it doesn't overflow. (The same note re: blackwater applies here if you're doing dishes by hand, or if you manage to disconnect the kitchen sink below a dishwasher outlet.)
• If you can't get to the sink pipes, consider placing a bowl in the sink to catch water when you wash your hands.
• Similarly, men can shave with a bit of water in a bowl instead of letting the water go down the drain.
• I think taking a bath is probably a bigger water waster than taking a quick shower, so I don't think it's worth switching to baths just so you can reuse the water, but if you do take baths, you can scoop out most of the water with a pail before opening the drain. (You'll either need someplace to store it, or you'll have to be able to use it right away though. And if you have little ones in the house, don't keep a tub full of bath water hanging around!)

Uses

• Any extra water can be used for flushing, but you should use the "dirtiest" water for this first since it is the last use that water will have. If you're storing the water in a bucket, you can just dump a gallon right into the bowl to flush.
• If you grab the soapy water from the washing machine, you can use it for washing dirty stuff -- scrubbing the toilet bowl, cleaning out trash cans, etc.
• The cleaner water can be used for watering plants. Be careful about what you use for cleaning products, and you can probably use the water on more of your plants. Be careful about what water you use on plants that you're eating directly -- I don't think I'd use bath water on my spinach, for example.
• If you have a top-load washing machine, you could pour in some of your cleaner water into the initial rinse water.
• If you want to all-out, you can build a slow sand filter -- even if you don't get the water back to fully potable, you can at least move it back up the cascade a stage or two. E.g. perhaps the washing machine outflow can be reused, assuming you can dump into a top-loader.