I have a tall vase with an unusual shape. The top opening is too narrow for me to get my hand, or even a large brush, into it. I left some flowers in there for a bit too long, and the inside of the vase is now pretty dirty. How can I get it clean?
There is a tool I use for these cases:
You can fit it into almost any vase, even if the neck curves.
Letting the vase sit with hot soapy water in it for a while can help too.
Here is a good resource for cleaning inside of containers: http://tipnut.com/how-to-clean-the-inside-of-bottles/
For something like this I'd recommend filling the vase with vinegar or vinegar and water and leaving it overnight :)
I use magic balls to clean inside vases and carafes. They work a treat, and you'll never need to replace them.
You just tip them in with soapy water, swirl them around, then tip them out onto a towel to dry.
Anytime I can't easily get inside of something I want to wash - it goes straight into the dishwasher. Easy peasy. Unless it doesn't fit, then as others mentioned some cleanser soaked and a some kind of elongated scrubber (hanger with a towel, whatever).
A good trick specific for wine vase (carafe), but that may also help for some other cases:
You can just use Coarse salt (gros sel) and a bit of water : put a small spoonfull of coarse salt in the vase, add some water (not too much, just enough to almost cover the salt) , and shake the bottle quickly using for example a circle movement (extend your arm and rotate your wrists, making the salt in the bottom of the bottle to quickly move around the vase) : it will scrub gently the deposits. Then just rinse the bottle out afterward, check if anything remains (and do it again if there was some).
Coarse Salt and Baking soda. They act well to both soak and scrub.
If the stain/dirt/refuse is more stubborn there is a more severe course of action: Household Lye
This is the stuff you might clean your pipes with. It is in effect Sodium Hydroxide, and creates a very strong base in water. It can literally dissolve the first few microns of glass from the surface. Be careful of fumes and do not allow this to get in contact with your skin.
To get rid of almost everything, especially organic, use hydrogen peroxide mixed with sulfuric acid. Both can be about 30% concentration and are good to keep in your garage for those purposes. Mix of these is called piranha solution and breaks down all organic dirtiness.
Hydrogen peroxide is sold in gardening supplies and paint stores. Sulfuric acid is also sold at paint stores and also as replacement acid for batteries.
Sodium lye is also efficient.
With those methods, use protection glasses and gloves. Gloves used for general home cleaning purposes will do. Those methods are especially good when normal soap solutions fail.