Flat rate boxes from the USPS is an easy way to know what shipping will cost before you mail it. If you sell books you can put in the ISBN and it will tell you information including weight, then you can go to the usps website and use a shipping calculator. For other things, you learn to judge the weight after you've been selling a while. You can also buy a postage scale at walmart.
Flat rate boxes are nice for small heavy things, but it is usually cheaper to just get a box and package the thing up the way it will be shipped and then weigh it on a postal scale. If you don't have one the post office will do it for you or buy one if you will be doing a lot of selling. When you are inputting the auction information a postage calculator will be there and you put in the weight and size and it will tell you how much to ship from your address to various other places. You can either choose to charge the exact shipping to the buyers address or enter a flat rate for everyone. I generally go with a flat rate to anywhere in the US and add $1 for handling and supplies like the box and tape etc.
Buy a Postal scale, they make traditional scales and digital ones, they weigh up to 50 pounds. When you list this you use "calculated shipping" and tell ebay the weight of the package and the methods you are willing to ship, then when any ebay member views your listing it shows then the exact shipping based on their zip code