Here are some of the freeware tools available to take care of the whole problem for you. Some are small sites whose creators have to ulterior motives. Others are giant corporations giving away passwords in the hope you'll buy their security software. Some are scam sites, so keep your eyes open.
For more security, if you're using a free online generator, it's probably safer to use one on a site you don't use, or for which you haven't registered. The less it knows about you the less likely it is to connect you with that password, just in case there is some ulterior motivation behind the free offer.
The simple way to choose secure passwords:
Use a secure password generator like the one Symantec keeps at PCtools. You can take the default settings, which usually default to a moderately secure password. Or you can click the little boxes that tell it to include numbers, letters, upper- and lower-case letters, numbers, punctuation and weed out combinations that are so similar you'll never type them right even if you're looking at them (lower-case l and 1, for example, or 0 and O, I and l).
Here are some other options. Try more than one. They're free, only take a second and all deliver pretty much the same product, so which you choose is your personal preference: