Some travel pillows are self-inflating, some use a small pump and some are blown up by mouth like a beach ball. There are also pillows stuffed with foam or other materials that remain permanently ready to use.
Inflating your travel pillow usually takes just a few minutes. Blow into the opening if you have a pillow that requires you to inflate it by mouth. You might need to squeeze the valve gently to allow air in. Alternatively, with many pillows you can use a small hand pump. These pillows have a small valve that you turn before using the pump. Some pillows are self-inflating, requiring you to just turn a nozzle to allow air in or out.