Flight
Most flights from America will likely connect through Madrid (MAD) or Barcelona (BCN) to get to Seville's airport. Or you can fly into one of the above airports and take a high speed train to Seville.
Train
There are two options for high speed trains that connect Sevilla to Madrid, Barcelona, and other cities: Iryo and AVE. Train tickets for Iryo are typically more affordable and can be purchased at the link below, and AVE tickets can be purchased through the company Renfe.
Travel Note
Seville is very walkable, so rental cars are often not necessary! Uber is commonly used. There is an above-ground tram and a below-ground metro as well, and even a city bike rental system.