Hungbonnie,
I've not traveled to Arcos de la Frontera but have visited Sevilla.
You can search for train schedules on Spain's official railway company :http://www.renfe.com/EN/viajeros/
According to Rome2rio, there's no direct train from Sevilla to Arcos de la Frontera. You'd have to take a train from Sevilla to Jerez de la frontera, then a bus to Arcos.
There's also a direct bus from Sevilla to Arcos but it only runs twice a day (11:45 & 18:00)
You can check the Los Amarillos bus schedules here: https://regular.autobusing.com/venta
You can only view schedules a day or two from today's date.
Since you'll be in Sevilla, have you considered visiting Córdoba? You can reach Córdoba very easily via high speed train.
Have a wonderful trip!
Edit to add: I forgot to mention...
You can book your train tickets 60- 90 days in advance at considerable savings.
You may want to read this article before booking your train tickets on the Renfe website.