When you click into a piece you're interested in, it should look something like this:
There are two ways to place a bid on this example Async art:
1) Artist have listed a "Buy Now" price, and if you have enough ETH in your crypto-wallet you can purchase the piece immediately for the listed amount. The transaction will take a few moments to process, but after it is done the funds will automatically be transferred out and in exchange the artwork will now be sent to your wallet.
2) Artist have also indicated a minimum reserve price for this piece. That signals the bidder should bid an amount above the reserve in order for the artist to seriously consider accepting the bid.
Type in the amount of ETH you'll be bidding with, click on "Place a bid" and let the transaction go through. Artist will need to manually accept the bid on their end, and once they do, an email confirmation will be sent to your account and art will automatically be transferred to your wallet.
If a couple of days go by without any action, it probably means the bid was too low. You can always withdraw your bid on the same art page, or increase your bid to have the artist reconsider.
It's also worth noting that your current bid funds are automatically sent back to you if you are outbid.