I've been doing Spring Training for the past 10 years or so. I've only missed a couple of years in that span. Spring Training is amazing, and everyone needs to check it out at least once.
It's hard to explain why I like it so much. For people that like meeting players and getting autographs it's great for that sort of thing. In it's own way, it's also fun to watch morning workouts. Games are great too as you get to cheer on the team, but aren't disappointed if the game ends in a loss. It's a celebration of baseball but with a great laid-back atmosphere. I truly love the concept of having no plans for a weekend except immersing myself with padres.
The padres ST schedule is over on the official website. Pitchers and Catchers report on Tuesday 2/12. Full squad reports on Friday 2/15. The first game is Friday 2/22 against the hated Mariners (this is actually and exhibition which doesn't count to Cactus League standings...an exhibition of exhibition). There are games practically every day in Arizona until Thursday 3/28. There are two games played in San Antonio, TX this year against the Rangers (3/29 and 3/30). On Thursday 3/14, the padres will play a game against one of the WBC teams (from the Asian bracket if I recall correctly).
Also in Arizona this year are some WBC round 1 games. Games for pool D will be held at Chase Field as well as Salt River Fields (Scottsdale). The teams in pool D are: USA, Canada, Mexico, Italy. The WBC games in Arizona take place from Thursday 3/7 to Sunday 3/10.
Sometimes it's just fun to watch baseball and not necessarily watch the padres. In fact, I usually try to schedule myself a double header on Saturdays. I'll watch an afternoon game and then watch a night game. There is ample time between afternoon and night games to grab a quick dinner and drive to the next venue. Anyways, you can check out a Cactus League wide calendar here, but be warned that it might not be up to date.
You may notice that some games are scheduled as a split squad (SS). Split squad games are when there is more than one game that day so that the entire roster isn't at the game. Usually the team is split into basically an A team and a B team with all the better players on the A team. There really isn't any way of knowing the roster of a split squad game well before it's played. I will say that I've noticed that the A team usually avoids travel.
All Cactus League teams now play in the Phoenix metropolitan area. The padres play in Peoria and share the Peoria Sports Complex with the hated Mariners. Peoria is a suburb in the Northwest part of town. The complex is at 83rd Ave and Bell Road. There is lots of shopping and dining in the area. Particularly across from the stadium on 83rd Ave and also all along Bell Road.
The road network in Phoenix is pretty easily navigable. Most of the city is in an East-West/North-South Grid. The streets that run North-South are typically numbered. The numbers are greater the farther you are from downtown Phoenix (Central Ave). North-South roads West of Central Ave have an "avenue" suffix while roads East of Central Ave have a "street" suffix.
Public transportation is pretty poor. Really just bus routes. There is a light rail that runs from downtown Phoenix to Tempe. The only stadium on that light rail route would be Chase Field (WBC) though.
Most stadiums have a parking fee, usually in the neighborhood of about $5. For Peoria, you can avoid the parking fee by simply arriving at the stadium early and watching morning workouts.
Tickets are very affordable, which is one of the things I love about spring training. I could never really afford to sit in the 4th row at Petco Park, but at Peoria Sports Complex it's a reality at just $26-28. All the stadiums are small enough that any ticket will provide a great view. A lot of the newer stadiums (including Peoria) have grass berms in the outfield. The grass is a great way to have a picnic and whatnot for under $10.
You don't really need to pre-purchase tickets. There are usually plenty still available on gameday. Some of the night games on weekends might sell out though. Also be aware there may be large crowds for games that involve the Doggers, Cubs, or D-Bags. [edit: some annoying dickhat (redundant?) on twitter decided it important enough to remind me that the Giants are also a big bandwagon team]
For lodging, I would recommend booking something before you leave. Rates don't go too insane during spring training season, but hotels can get booked full on the weekends. I like hotels.com, but any search site is fine. I've never been creepy enough to confirm, but I think the Padres players usually stay at the La Quinta on 83rd Ave next to the stadium.
I don't know how it works for other teams, but workouts are easily accessible for the Padres. Every morning (10am I believe) the team will do workouts. The players will arrive 30 minutes to an hour before that. There is always a handful of autograph seekers waiting at the gate to the players parking lot. The major leaguers will be on practice fields 1 and 2. There are some metal grandstands, but seating is pretty limited. It can also be a little tough to find some shade at times.
Watching practice is free and you are allowed to bring food and drink in. There is a small snack bar too if you didn't bring any of your own. Park in the parking lot to the East of the stadium (outfield parking lot).
The ticket office and the team store are usually open around 10am as well. Both are on the other side of the stadium of the outfield parking lot. Fortunately, there are usually volunteers on golf carts that are happy to give you a ride to the other side of the stadium. All the volunteers at Peoria are really nice. In fact, the guy at the practice field gate likes to give out lollipops to children as they arrive.
For autographs you have a few options. As mentioned before, sometimes you can get some players as they drive into the player parking lot. There is also a designated signing alley between the clubhouse and practice field 2. Also, you could just get a player's attention while they are on one of the practice fields. Once inside the stadium for game-time, there is also an autograph alley between the clubhouses and stadium.
Workouts usually wind down around noon in order to prepare for the game at 1pm.
FOOD AND DRINK
I'm not going to be much of a help on this section. Mill Ave in Tempe is a big nightlife/bar area as it is right next to ASU. It's a bit cheesy, but I like Alice Cooperstown in downtown Phoenix; it was featured on Man vs Food for their 22 inch Big Unit Hotdog. There's all the chain restaurants you could ever hope for right next to the Peoria Sports Complex (Cheesecake Factory, Texas Roadhouse, Buca Di Beppo, Elephant Bar, PF Changs, Hooters, Tilted Kilt, In-n-out, Chick-fil-a, Red Robin, Applebees, Denny's, Del Taco, Jimmy Johns, etc.)
There's a movie theater right across the street from the Peoria Sports Complex. There's also another movie theater a block or so away on Bell Road as part of the Arrowhead Towne Center mall.