Most of the multiple offer situations are bank-owned (REO) properties that have just come on the market. In many cases you have to see the property as soon as it comes on the market and submit an offer right away. There is no waiting until the weekend to see a "hot" property.
When making your offer you need to think about 2 things. The first is how much would this home be worth if it was in perfect condition (take to your REALTOR for help with this), and how much money would it take to do the required work? Take the value of the home and subtract the cost of getting it there and you will have the market value of the home in its current condition. Many bank-owned properties only need paint/paper and minor repairs. You then have to decide how much under (or over) that market value you want to offer.
The second thing you have to think about is how much is the property worth to you? If you like the property but it isn't your ideal home, its not going to be worth as much to you and therefore you may want to submit a lower offer. But when your offer gets beat out by another buyer don't say you wish you made a higher offer. In most cases you only get one chance to make an offer on a bank-owned property, and the highest/best offer will be accepted. Occasionally in a multiple offer situation where all or most of the offers are around the same price the seller (bank) will come back to all buyers and ask for their "final and best offer". This is a form of counter offer where you get a chance to up your offer one last time (or leave it where it is).
Make sure that you have a mortgage pre-approval letter in hand before you make an offer. You will not have time to call up your mortgage person to obtain one, and your offer will not even be considered without it.
You really need to work closely with your REALTOR to successfully get through a multiple offer situation. Even with all these considerations you may still get beat out by another buyer who really, really wants the property. Don't dwell on it...just move on. It happens. Just remember that the price in your offer is the main deciding factor with any seller. Good luck!