Public courts are rare in Mexico. Mexico has a lot of private clubs, where guests are usually welcome. These clubs don't do much in the way of publicizing their existence, so you'll have to do some asking around.
“Deportivos” (sports clubs) are more accessible. Usually, you pay a day fee of 100 to 150 pesos at the entrance. This fee covers all the club's facilities, so bring your bathing suit. The “Club Britania”'s found in many Mexican cities are actually deportivos.
Ball boys are commonplace wherever tennis is played. This is something easy to get used to; they speed up the game considerably. You're expected to tip them; the going rate is ten or 15 pesos per player per set.
If you're going to a high-altitude place such as Mexico City, Oaxaca de Juarez, or San Miguel de Allende, don't bother to bring balls with you. Only pressureless (“sin presión”) balls are legal in these areas. The most common brand is Tre-nis (sold as Tretorn in the US and Canada), but pressureless balls are easy to spot on store shelves; they're sold in cardboard boxes instead of cans.
There are clay courts (“canchas de arcilla”) in Mexico, but they're gradually going the way of the dinosaur, due to maintenance costs. Hard courts are called “canchas duras”. You may come across synthetic turf courts; I suggest trying to avoid them.
Las palabras importantes
Here's a crib sheet on a vocabulary that's useful when playing tennis in Mexico:
deuce: iguales. You'll also hear “quince iguales” for 15-all, and “treinta iguales” for 30-all.
Advantage: ventaja. This gets interesting. Server's advantage is “ventaja al servicio” (or “ventaja dentro”) and receiver's advantage is “ventaja al recibir” (or “ventaja fuera”). These terms aren't commonly used, though. If you're playing singles, you would hear “ventaja mia” (my advantage) or “ventaja tuya” (your advantage). But, if you're playing doubles, you would have to use the plural form, which is “ventaja nuestra” (our advantage) or “ventaja ustedes” (your advantage).
Set is the same.
Let is also the same, but on a serve, it's more common to respond with the number of serves remaining: dos, uno, or doble falta. “Let” is still used when a ball comes onto a court that doesn't belong there, or for some other interruption of a point in progress.
Tie-breaker: muerte súbita (literally, “sudden death”)
Out: holding up an index finger works, but verbally, it's salió or fuera.
If somebody says ¿cual es?, ¿como vamos?, ¿como es?, or ¿cuanto va?, they want to know what the score is.
The most common word you'll hear from your partner is cambio, which means, change sides. If he says, fuera, it means, don't hit the ball, because it's going out. I've found that the phrase “I got it” is understood worldwide, but mía!, yo la tengo!, and voy! are correct Spanish terms.
Other useful words
Service break: romper de servicio
When you spin the racquet to determine who serves (saque), it's arriba (up) or abajo (down).
Tennis for spectators
If you enjoy watching tennis as well as playing it, The Mexican Open in Acapulco at the end of February is well worth going to. It attracts a lot of good players, is at a high-quality facility, and is well run. After that, there's a series of ATP Challenger tournaments close together in geography and time: San Luis Potosí (clay), León (hard), and Guadalajara (hard).