You will have to buy a new drive. A dvd-rom (read only) cannot be upgraded to become a burner. Even if you have a combo drive, one that reads and writes cds, but only reads dvds...they cannot be upgraded to burn dvds either.
Look on the back of the current drive and see what type of connection it uses. Older drives use an IDE cable, which is normally gray, wide and flat. Most of the modern drives use SATA connections, and have a much smaller cable, often times colored red.
This will tell you what type of drive to purchase as a replacement. A good SATA burner would be something like the Optiarc 7240s. You can find them in the US for less than $30 usually, at online shops like Newegg.com or zipzoomfly.com.
IDE interface drives are getting a bit scarce. Here is the list of available ones at Newegg: http://www.newegg.com/Product/ProductList.aspx?Submit=ENE&N=2010100005+1038406818&QksAutoSuggestion=&ShowDeactivatedMark=False&Configurator=&Subcategory=5&description=&Ntk=&CFG=&SpeTabStoreType=&srchInDesc= If you do have an IDE interface drive now, make sure to look at the little jumper on the back of the old drive and put the jumper on the new dvd burner on the same setting. It will be M (Master), S (Slave) or CS (Cable Select). SATA drives do not have master, slave or cable select settings, so not something you have to worry about with them.