This is a normal issue and it actually got me several tries to figure it out.
Thing is that there is a strange "lag" when you try to take personnel "on" vehicles. You need to go to the vehicle screen, select your squaddie then drag and leave them on the desired vehicle. You can move several squaddies at the same time by selecting them all then dragging one to the desired vehicle.
Then, you need to select the vehicle in particular in CityScape mode and either send the craft to the desired building or to the crashed UFO.
The smaller and lesser UFO's are unmanned and won't require a fight. You'll just recover them. I usually only capture one of each of the smaller UFO's and then don't bother and make them explode in the air when I encounter them.
From past experiences, I am pretty sure that it does make a difference when you actually destroy Alien Ufo's. It doesn't take them much time to build new ones (perhaps a month max for the bigger ones?) but it does seem to buy youself some time and change the way the AI act. If you are very successful at the beginning, you will encounter a lot of bigger and bigger Ufo's until your current technology can't fight them without stupidly high losses. But then again, when you grab their own technology it really give you a boost!
The best strategy I have found so far to fight those Alien crafts is to take something like 5 Hover Bikes and set them to fight at the highest elevation possible and as close as possible to the target. You can change the stance of each craft when you select them on the CityScape. The Hover Bikes are stupidly hard to hit for the Aliens because they are so small and so maneuverable, and most of the time the Hover Bike will simply dodge the beams which would have teared your biggest ships appart without a problem. This allow your bigger ships (like the Phoenix Hover Car for example, which is cheap but virtually armorless) to stay further the front line and throw missiles from a further distance. Most of the time they won't even come under fire unless you are really fighting lots of UFO's at once.
Also make sure that your Troop Transport is far from the action and safe. It's easy to lose it to bad luck if several Alien Crafts decide to fire at it at the same time.
Usually, I always make crafts which are 50% to retreat and repair. Crafts cost a lot in this game and losing them only to down a Ufo is not worth it. You can still use a craft being repaired on an emergency mission later on, and if Air Superiority fail then send your squaddie and eliminate the Alien threat from the ground.
The strategy mentionned above (with Hover Bikes) works quite well against Metropolis crafts as well, but is less effective due to them almost always having aiming missiles equiped and due to the fact that they are more maneuverable than most UFO's. They also really pack less of a punch, so unless you are unlucky retreating at 50% health will usually save your crafts anyways.
Don't overlook the Hover Bikes power. Their seemingly powerless guns really add up when they team up. Have 10 of them and you'll see them tear into a bigger UFO shield in no time. Plus they are really hard to hit and are cheap to replace.
Random tip #2: Always upgrade the biggest engine available to each of your craft. If you buy a bunch of crafts at the same time (or at the beginning of the game), you can actually take the engine of one craft and put it in another knowing it's the most powerfull one they can bear (because of the size of the engine square). For example, if I remember well the Phoenix Hovercar engine is the biggest engine a Hover Bike can be equipped with, so don't sell those and use them on the Hover Bikes you'll purchase. I think the same thing happen to your troop transport VS your Phoenix Hovercar but I don't remember well. Anyways, reason for this is that you want power and speed, and since you will be placing aiming equipment on those crafts and that it add weight and lower your engine power and acceleration (slightly), you have no choice if you don't want to suck the UFO's exhaust vapor trail. It also greatly help in combat. Maneuvrability is really your friend until you build your own crafts later in the game since your craft armor is very weak against the Aliens weapons.
Random tip #3: always make your crafts to fly and fight at the highest altitude unless you have a really good reason to do otherwise. Until you actually fight with beam weapons yourself, the aliens have the bigger guns... And a stray fire from those babies if it hit the base of a random building will usually result in having the building flattened completely. This will irritate the leaders of that faction to no end, taking their strance VS Xcom down each time. Plus the Government (which fund you) always get angry when anything on the city is destroyed and this goes against your weekly score. If you fly high the UFO usually fire at your upward, and you can save friendly fire this way.
Of course, some members of the "Cult of Cyric" sometime accuse Xcom to fly around their buildings in purpose when fighting bigger Alien Crafts... Which always been soundly refuted by the Xcom Leaders. That's what war is about, you
will have friendly fire sooner or later... ... ... Ahem... :whistle:
Happy hunting!
[Edited for grammar and syntax errors... One of my earliest post...
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