There was a big thread, or could have been an old FAQ post, on this some time ago, but the basics are as follows (as Neil suggests, if you could post more details about your specific need, I'm sure someone can give you some first-hand advice);
1. Cash upgrades
Assuming there is space available, these are the ones that are almost always available, however rarely is this the cheapest option. Unless they have an operational need to bump a few people up, you'll be paying the difference between the price you paid and the cheapest seat available in the cabin you want to upgrade to - and if you're buying that at the airport, the discounted fares won't be available. So, ouch, basically.
2. Miles upgrades
You can normally upgrade at the airport for the normal one-way mile cost, providing your ticket is in an upgradeable bucket class and there is space in the cabin you want to move to. Upgradeable bucket classes are Y, B, R & L in Economy, and W & S in Premium. If your ticket isn't in one of those buckets, you can pay to upgrade your ticket to an upgradeable fare, then use miles for the cabin jump, but only if all the buckets are available.
3. Involuntary (Free) upgrades
For all sorts of reasons, but mainly because they have more people turn up for a seat in Economy than they physically have, VS will need to shift a few people up into available seats in higher cabins. Typically they will either offer a special price at check in, or they will 'involuntarily' upgrade selected flyers. These selected flyers will normally be VS Gold card holders or staff. However, involuntary upgrades are getting rarer, even for long-term Gold carders. And there's little point asking for a free upgrade at check-in. If they're planning to move you, that decision will have probably already been made by the airline some time before you approached the desk. Involuntary upgrades are nice-to-haves, but don't count on them. If you actually want to fly in the higher cabin, the rule is, as always, buy a ticket.
