Spawn manipulation is not intuitive but easy once you know how.
A quickstart guide.
I'm assuming here you are lone-wolfing and only interested in finding good fights rather than organised group play or playing objectives. These are best done by finding an outfit or joining one of the big outfits public squads on that screen, then following orders till you understand why those orders are being given.
As soon as you log in open the mini map and press Instant Action. This will zoom you to a location and give you a 10 second countdown till it drops you onto it. Use this time to assess the fight by mousing over the hex and viewing the information it brings up. IMO the best for new players would be a 24-48 population (on each side) with a no more than 10-15% population imbalance. Any more imbalanced than that and it is a spawn camp. Any more players than that and it is a zerg fest clusterfuck where you won't have a clue what is going on and only serve to be more cannon fodder. Finally look at the base capture timer. A long timer (10+ minutes) is a potentially great ongoing fight with a running defence in the open and relatively well defined positions and battle lines. A short timer (< 2 minutes) usually means the base is camped and falling soon, although not always. No timer or a timer somewhere in the middle can be a crapshoot, but you can often guess the situation based on the populations.
If the fight looks good, drop on it and enjoy.
Also note that if it drops you on an enemy base then there is a chance you won't have respawn options in that hex and might have to fall back to the rest of this guide. Hopefully there will be Sunderers and outposts nearby you can spawn at, but this isn't always true.
If IA looks like a bad fight then cancel it and assess the continents. This is hard if you are new and don't know all the details, but generally you can get an idea of how much territory you have and what the overall population is like. If you are overpopulated on a continent and don't hold much territory odds are there are some big zergs going on capturing bases. This is generally hard to catch up with as a new player and not fun unless there is a lot of resistance. I tend to ignore these unless they form up around me.
A continent with low population but plenty of territory would be my choice. These let you fight a series of running defences (with associated defence and population XP bonuses), picking your bases and more easily spawning where there is an attack. Still, you will get spawn camped quite a bit, so may not always be as fun as advertised.
A straight 33/33/33 pop balance with a reasonable split of territory (eg, Indar during prime time) is always nice, but be aware the battles will be huge zerg fests most of the time, occasionally with organised outfits dropping in to tear through them. These can be great fun depending on where the battle lines are.
Once you've picked a continent, hit the delete key (I think this has been remapped to u recently...) to redeploy. This is your main logistical tool. If you are in a rush you can type /suicide. This will save you the 10 second coutdown and instantly start the 15 second respawn counter, which is nice and fast, but will count as a death on your KDA if that kind of thing bugs you.
As for where you can spawn, it's a bit complicated. I'm just going to
quote here;
You can always spawn at your faction's warpgate.
You can spawn at any Sunderers within 1000m.
If your faction controls the outpost in the area where you died, you can spawn there.
If your faction controls any neighbouring outposts, you can spawn there. (On lattice-based continents, "neighbouring" uses lattice links. On hex-based continents, this uses map hexes.)
You always have access to the nearest major facility your faction controls. ("Nearest" is determined using either lattice links or map hexes, depending on what continent you're on.)
Finally, the top three Instant Action locations are added to the "Reinforcements Needed" list. The algorithm that determines these spawns isn't entirely clear, but it tries to select outposts with active fights where your faction is at a slight disadvantage. (What constitutes an "active fight" and a "slight disadvantage" is frequently tweaked from patch to patch.)
If you are in a squad, the friendly facility closest to your squad leader and any squad beacons are added to the "Squad Spawns" list.
I've checked this against the patch notes I can find and it all looks correct. Note that the squad leader spawn point overrides your closest spawn point as the default, so just spamming respawn while in a squad can often have you ending up well away from the front lines when your leader had fallen back to grab a new vehicle. I avoid this kind of thing by deploying by double clicking on the actual spawn points on the map rather than the respawn button. Also nice to avoid that useless Sunderer someone has parked under a biolab.
Generally I'd check the Reinforcements Needed bases first. This is a crapshoot, but often gives you a reasonable fight (using the same assessment as the IA fights). The next option is to deploy as far forwards as possible (usually a major facility or just one of those Reinforcement Needed bases where I'll never actually leave the spawn room) and redeploy again from there. If that's still going to take ages then I hit the insert key and see if joining a random squad will offer me any new respawn options. You'd be surprised how often this works.
If you can't get straight to the front lines then hit delete the instant you redeploy (eg, the instant the loading screen comes up). This will start the 10 second countdown even as you are loading the new location and let you redeploy again far more quickly. I can usually reach a fight within three hops even if it's a horribly long distance.
Again, if you are going on the offensive you should be starting in a nice group. Usually a counter-push against a failed enemy attack in my case. I'd recommend trying to get a gunner position on either a main battle tank or Sunderer for your first big pushes. Pulling your own vehicles should wait till you have seen how these pushes go.