In La Latina are some of the most famous places in Madrid for eating "huevos estrellados" (fried eggs with French fries).
Casa Lucio (calle Cava Baja 35) is without a doubt the most famous. Traditional, with excellent service and food, it is very popular among the famous and not so famous of Madrid. For this reason, reservations at least a week in advance are a must (91 365 82 17 or 91 365 32 52). Get the fried eggs and French fries at 12€ as an appetizer to share and the "chuletitas de cordero" (lamb chops) at 18€ for the main course. Lunch will run you around 30-35€ per person. Closed in August and on Saturdays at midday.
If you can't get a reservation at Casa Lucio, you can always go to Taberna Los Huevos de Lucio (Cava Baja 30, in front of Casa Lucio). Run by the same owners as Casa Lucio, the quality of the food is very similar. While you'll probably have to wait to be seated, you don't need to make a reservation.
Very close by is El Almendro (calle del Almendro 13), where the atmosphere is relaxed and the prices are less steep. It's tough finding a table but if you're patient, you'll eventually be seated (there's also space in the basement). Orders are placed at a window on the upper level and drinks at the bar on the way down to the basement. Get the "huevos rotos" (broken eggs) (8.80€ for a full order - 5.50€ for half an order), the "almendrito de jamón" (3.20€, available only for lunch) and the "pisto con huevo" (ratatouille with eggs) (8.80€ full order - 5.50€ half order). For dessert, try the traditional "tocino de cielo" (3.80€). Draft beer: 1.50€. The whole meal will run you about 15-20€ per person.