Clean glasses are really important for enjoying wine. It's not rare to encounter smelly glasses that make it hard to appreciate the aroma of a wine. This is especially common where you are faced with a flight of several glasses: the more glasses are used in a tasting, the harder it is to ensure that they are really clean.
I'm quite obsessional about washing glasses. This is how I do it:
1. I use a cloth and lots of hot soapy water. I know some people don't like using detergent because of worries about residues, but unless you use soap it's hard to get the glass really clean, especially if it is a bit greasy.
2. Then I wash the glass out with lots of hot water. Lots and lots. Soapy glasses kill wine.
3. I don't use mineral water to do a final rinse with, so I have to make sure that the glasses are dried properly. I use a microfibre glass cleaning cloth (here), which does the job really well.
I wouldn't use a dishwasher for wine glasses. I'd also avoid turning them upside down on a cloth to dry them: this can make the rim a bit smelly. It's really worth the effort of washing glasses well before you put them away, because then you can use them without worrying about whether they are going to be smelly or not. If you are in doubt about a glass, a quick rinse with wine primes the glass nicely.