A couple hard-learned single-player hints for the first day (or days if you're like me and took a few tries)
edit: found a couple more tricks which makes life a bit easier, so re-writing this to be a bit more detailed.
(To avoid saying "in the current version" every time, this was written Aug 2014, pre-v3. In the future mileage may vary)
Rule 0: Zombies have a fairly defined detection radius. It's never a bad idea to work around the outside of the town, letting a single one "find" you, and taking them out before moving on to the next one. It is almost always a bad idea to run through town triggering multiple zombies to chase you. (Or using a firearm, in most cases - the sound can easily bring more zombies than you can handle.)
Rule 0a: Zombies either respawn very slowly or not at all, until you disconnect. Then, everyone respawns. This means you want to disconnect/restart as little as possible, and you want to be in a safe space (for beginning the game, away from civilization) when you do disconnect. When night falls, the best thing to do is retreat to wilderness and just wait it out (I tab to another window and wait for light). Items in town do respawn, so being able to safely ransack the cleaned-out town multiple times is huge.
OK, so now, let's get you started.
Step 1: You need a melee weapon. Anything will do - golf club, baseball bat, frying pan. Right now you do not have the luxury of being picky. You're going to have to fight the first few zombies with your fists, and it sucks. You want something swingable ASAP. Sadly, there's a bit of a catch-22 here. You need a weapon to efficiently kill zombies, but all the weapons are surrounded by zombies. Best advice I have is work around the outside and check the buildings on the outskirts and hope you get lucky.
Important: right now, you can carry exactly four things (and realistically should only carry three to avoid shuffling inventory around). So ignore anything that isn't going to keep you alive for the next three minutes. The one exception is clothes (since you can wear them and that doesn't take up a space).
Step 2: You need a pack. Again, beggars can't be choosers - it's nice to get the Alice Pack (or even a Rucksack), but even the basic schoolbag and it's four extra slots makes your life much easier. Now that you have a weapon, cleaning out the town is much simpler - trigger zombie, wait for it to approach, right click on it's head to power-attack, step back and repeat till it dies (most weapons will kill a zombie with one power attack headshot, but better safe than zombie food).
Step 3: Food and water, and "shelter". Once you have a decent weapon and a pack, you're in decent shape. But finding non-moldy food and water is tricky and the lack of either will kill you just as good. So, we need to start finding secure sources for both.
I have "shelter" in quotes because in single player a safe haven is "anywhere the zombies aren't, and that I can find again". I usually pick an overlook for whatever town I'm in - far enough away that the respawn doesn't swamp me in zombies (right now I log in, kill a single guy, and I'm good), but that I can easily find from the town.
But here's what you're looking for with your new pack:
a) A canteen. (Or a water bottle and a can, which lets you craft one). Thirst really sucks until you have one of these, and then it's trivial. Canteens hold water and are refillable at any source of water (ocean counts!). So, you fill up a canteen, wander around, and when you get thirsty you find the sea, refill, drink, refill again until Thirst = 0.
b) Seeds. The wiki is a bit misleading here, talking about fertilizer and such. Food is pretty straightforward - pick up some veggies (moldy is perfectly fine). Craft them into seeds. (Fresh veggies give you two, moldy gives one). Go to your shelter area, plan them in the ground - the game will tell you where you can or can't, but pretty much anywhere grassy works. Go about your day, come back in a bit. (I haven't timed it exactly, but the grow time is crazy short - under a day. Harvest, pick up your now fresh veggie, craft it into seeds, replant. In short order you'll have more food than you know what to do with. An added bonus here is that planted food appears to survive disconnect/reconnection, which means even if you die you've got a garden waiting for you when you return.
Now, the big question: can you get this all done your first night? There's a lot of luck-of-the-drops here. There's enough melee weapons that you should be able to find something. Moldy food is pretty common, so getting a garden running is a safe bet for day 1. Canteens are rare-ish (and water in general, I find), so pick up any you find (even pre-backpack!). Backpacks are hit-and-miss. Sometimes there's none, and sometimes every house has one. I'd call my day 1 a success if I find a decent weapon, get a couple seeds in the ground, and find either a pack or a canteen. Once I have both, life gets so much easier.