Yes you can use both wired and wireless at the same time. You just need a modem either with wifi built in, or you need to connect the modem to a wifi access point or wifi router. Your computer, phone, or tablet also have to have a built in wifi card to use wireless internet.
Most modems nowadays have both a ethernet port (wired) and wireless. You can use both at the same time. You simply plug an ethernet cable into the modem port at one end of the ethernet cable and into your computer-ethernet-port at the other end of the ethernet cable.
Setting up the wireless is a little bit more tricky, but it is just simply turning on your wifi antenna in your computer (almost all computers except the most bare-bones-budget models have wifi cards built in).
Some modems are only wired and they don't have wifi built into them, but you still can get a "wifi access point" or "wifi router" and plug that into the the modem (normally with an ethernet cable), and then you have wifi too.