bearcat33: When the game announces that one of your bases is being invaded, either delegate the defense, or ignore the situation.
Why? If you try to defend the base, the game tosses your soldiers across the whole base at random, far apart from each other.
The aliens evidently can walk through walls. They can and will show up anywhere, they don't have to use the base entrance. So, you cannot lay a trap for them, even if you do manage to get most of your men in one place.
Also, the game gives the base-invaders insane firepower that will cut through your men like they were made out of tissue paper. Your weapons, on the other hand, will seem to bounce off them.
It's agonizingly frustrating, and just not worth it.
Let them take the base. Opportunities to re-take it will eventually arise, and you will be able to group your men for the invasion. Defense is a losing game, big time. A major flaw in the game, IMO.
Caveat: I have been completely unable to make any charachter throw grenades. The interface for throwing grenades is insanely difficult and I gave up quickly any attempts to master this messed up proceedure. YOU may have great success defending if you use grenades, but I doubt it.
The invader armor has been shrugging off their own rocket rounds! WTF.

Collie: Are you talking about Aftermath or Aftershock? In the Aftermath game, your soldiers are indeed split up. You must quickly gather them together immediately. Waste no time and try to avoid too many open areas along the way. Look out for opened doors - this means the invaders have been there. Avoid fire fights also. Once your men are assembled together, you can start to slowly track down and kill the aliens.
If you are finding your firepower is weak, you need to adapt to the situation. In base missions, always have your rifle troops carry a spare shotgun. Switch to the shotgun whenever you are going around a corner or entering a tight space. Shotguns will obliterate all but the hardest of aliens at close range in just a few shots. For weaker troops, make them carry a sub machine gun and have them use burst fire when you expect trouble at short range. If you see too many aliens about, hide round a corner and wait to unleash hell when the alien chases after you. Base defence missions are fairly simple affairs after a time.
If you are on about Aftershock, well I imagine base defence missions are trickier still, but many of the same things apply. There is strength in numbers, and you still need to get as much firepower centred on one area as possible to kill the aliens so avoid open fire fights where your firepower is limited to long-mid range snap shots and there are lots of aliens about. Unlike in Aftermath you can't have all troops firing at the same target if you have friendlies in the way which means you need a bit more tactical sense and possibly luck.
For grenades, don't you just have the grenade ready in your weapon hand, then right click on the area to throw? If not, try pressing 'A' to put the cursor into attack mode, then select where you want to throw it. You might struggle to throw the grenade far though. Alternatively there is a throw command, but that might throw the grenade unreadied.
Good luck.

jpm500: New to the game.
I found grenades annoying at first. The first trick was to let the soldier go through the animation to change weapons. I would often change inventory around and then issue a new command (I think after clearing current commands) and the soldier wouldn't change weapons.
Next was that I had to click the attack button (or press A) then target the area. Probably in the manual but I was just trying to play intuitively first then go to the manual when I could get more out of it.

Collie: Ah if you are that far into the game, then yes, base missions are a nightmare. Rocket launchers and warp weapons ruin the game. The only real defence is the aforementioned collapsable weapons (although your own custom Plasma weapons aren't bad). The best seems to be the machine gun variant which has 60 bursts IIRC which is usually enough to last the entire mission. Set it up at a junction and get everyone to rally around it. Two or three collapsable weapons will probably win most missions with minimum effort. I don't recall ever noticing aliens walking through walls, as they all use doors to get around. They just spawn at random points it seems so you have a nightmare tracking them down. Their behaviour can be predictable after a while, although sometimes they can wander off and hide which is annoying.
Basically once you have collapsable weapons you better start deploying them in every base and ufo mission. They are the only weapon that can deliver the firepower you need quick enough to stop your troops all being wiped at in a micro-second. For me, this point is where the game is boring and mostly pointless. It's one repetitive mission after the next until you reach the rather rubbish end mission.

bearcat33: What makes me rip out my hair most about weapons is Psi weapons. COMPLETELY USELESS. They NEVER EVER work. Same with PSI helmets. Utterly useless.
I feel like I've been raped by this game. Hours of my life wasted. It looked like I'd love this game.....I LOVE the ability to control game speed, and like other aspects.
But the "defend the base" missions are just too poorly balanced.