Find the Night Shade TM

There are a couple of methods available to increase your likelihood of encountering a shiny pokemon.

Capture All National Pokédex

Method: Finally, when you manage to capture all the Pokémon in the National Pokédex (not counting event legends) and show it to Cedric Juniper, he will tell you his daughter has a present for you.

This present is the special Shiny Charm. This item increases the likelihood that you will encounter Shiny Pokémon. When you have the item in your bag, then the chances of encountering Shiny Pokémon in the wild is increased to 33% of normal, making it a 1 in 2,370.6 chance. If, however, you\'re using the Masuda Method to breed, it increases it from 1 in 1,365.3 down to 1 in 1024.

Source: Serebii

The Masuda method mentioned above can also be used without the Shiny Charm:

Rather than encountering Shiny Pokémon with a probability of 1/8192, the Masuda method lets players breed Pokémon of differing real-world geographical origin with a 5/8192 (Generation IV) or 3/4096 (Generation V) probability of being Shiny upon hatching.

Well, you can't over write the save that is already on the game, which you got the warning message about when it said" "please press SELECT+UP+B at the start menu." so, if you want to save in game you have to start again and follow that command to be able to save after.

With the legit version of black I had the same problem, I bought a 2nd hand version and I got to the first gym and couldn't save, I had to restart the DS delete the save file and then I was able to save.

Direct Answer

No, you can't you have to start the game but before you can start a "New Game" you have to follow the "please press SELECT+UP+B at the start menu." command