I'd like to connect my Magnavox Blu Ray player (Model No. NB500MG1F) to my wireless network. Can I do this using a network adapter?

Check within the settings menu to see if there are wireless adapter settings if a adapter in not installed in your player you will need to contact the manufacture to see if wireless is supported on this device. If it is you should buy the adapter sold buy the manufacture. DVD players and set top boxes run software specific to the device and there is usually no easy method to add drivers to support hardware options and configurations not supplied by the manufacture. Many set top boxes and other appliances use some variation of Linux and several devices have been hacked you will need to do research to see if your model is one. This model has been offered by several large retailers at a low price for a Blueray player so there should be a lot of them out there maybe someone has hacked it.
If a factory supported wireless card is not available you can use wireless bridge placed near the player and cable from bridge to player.