Welcome Irene! There is actually a great thread for newbie giveaways here.
And for more immediate replies (people check help more often than other threads) you can also try the help forum here.
How do you bid on pet auctions?
Go to Trading -> Pet trades and choose a condition to sort by, such as "Time Remaining" and click that to sort either by longest or shortest auctions. You can also hit the square that says "show only lots with buyout" to just buy pets directly instead of bidding on auctions.
If you find a pet you want to bid on, click the name of the pet. (I suggest opening it in a new tab if you don't want to lose your place.) Then, scroll down the page to see "Your Bid" in big letters and enter a number you wish to bid. If you do not win the pet, the silver will be returned to you. Otherwise there is a "Buyout" button next to the "Place Bid" button to just buy pets listed for a buyout price.
How do you get vermillion?
1. In explore. Volcano is good for this. I recommend using a building called the astrologist to help find vermillion.
2. Trade for it! Use item exchange to trade goods for vermillion.
3. Sometimes you can buy it in the auction house. (Items, not pets.)
4. Battlefield- Not a reliable or easy way, but you can get vermillion by holding certain points on the battlefield but it's only 10 at a time.
5. Make friends and offer to trade for vermillion directly.