Seville to Lisbon

The best way would be to fly, but this isn't always the cheapest option. See www.skyscanner.com. If your schedule is flexible, play around with the dates to see if one day of the week is cheaper. The least expensive option is to take the bus. There are 2 buses daily, leaving Sevilla at 15:00 & 24:00, both taking about 7 hours. Tickets can be purchased a day or two ahead at the bus station in Sevilla. See www.alsa.es for details.

Without knowing what you want from 'best' and to give the third option, overnight train - www.renfe.com

The night train can be a good option, but just to clarify, it leaves from Madrid, not Sevilla. There are high-speed AVE trains hourly to Madrid from Sevilla taking about 3 hours. The night train, #332, takes 11.5 hours, departing Madrid at 21:05, arriving in Lisbon the next morning at 07:30.

I've done that trip in the opposite direction; and I can testify that the buses are quite comfortable. However, with advent of budget airlines, I would definitely check out that option. Vueling? I, myself, would not want to use up one of my precious vacation days taking a train to Madrid, etc. And if you've never taken an overnight train, you should know that many people find it VERY hard to get a decent night's sleep on them.