If you want to fix the strap on your ski goggles, you shall first take off the strap from your goggles. Observe the strap and determine if it can be fixed. If it is badly broken, i suggest you buy another new strap instead. If the strap can be fixed, you shall first cut off the broken part of the strap and remove the damages material. Then, use a sewing machine to join the two overlapping blunt ends. Then install the strap on your goggles to see if it comfortable to wear.
If you can find a profession sports shop in your neighborhood, you'd better take your goggles to there and have them to repair it. If you can't find one, the first things is to check the strap whether it is too damaged. If it is too damaged, you need to buy a new one and then change them. If it is not and you can fix it by yourself, you need cut off the torn portion and then end up with two blunt ends. You should make sure that you remove all the damaged parts. Use a sewing machine to connect the two blunt ends. You should do this step several times to reinforce them. The last step is adjusting the strap in order to fit for your head.