One strategy that never fails to be effective against any defence is the über rush. The offensive team has the same setup time as the defensive one, and medics can use this to fully charge their übercharge. Since the December 20th 2007 update, medics now heal everyone fast enough during setup time to fully charge their übercharge before the fighting commences, so at least 2 or 3 medics should be charged when the initial assault begins. Same goes for the defence however, so watch out for the defensive counter-übercharge that will probably be activated just as your’s starts running out.
There should always be at least one über rush at the start of each stage – the defenders get time to set up defences, so the attackers should get something as well. The question is what class should receive the übercharge? More often than not I find the heavy is quite ineffective at this, since a rush is supposed to be fast, and although he can make defenders flee, they simply return when his invulnerability wears off. Instead I recommend a pyro rush (mass panic and effective at taking down turrets, clearing out defence for his teammates) or a demoman rush (free to sticky bomb every engineer and building he sees, greatly reducing defensive effectiveness). The best option is probably to do both, which requires a recommended 2 medics.
Best case scenario is the über charge decimates the defence and the survivors can be mopped up by the full strength attacking team, leading to the easy capture of the first point. However if this level of success is unattainable, at least try to take down the sentry guns, dispensers and demomen/medics, since these are the defence’s most valuable assets. After the rush it is just a matter of pushing forward until the enemy collapses. This is greatly aided by one or two good spies removing teleporter exits (entrances first if the exits are well guarded) and stabbing key targets like medics and heavies. DON’T fall into the trap of having too many spies – not only are 4 spies barely more effective than 1 or 2, but the defenders will grow accustomed to the constant swarm of spies and become very paranoid (that’s bad).
Assuming your team doesn’t have too many spies/snipers/scouts, you should be able to follow these guidelines and take the first point reasonably comfortably. The second point is always the hardest because it is right outside the defender’s spawn, so they can respawn and defend much faster than you can respawn and attack. Often the main concern of attackers is the sentry gun spam which always seems to occur, since engineers are not required to move once they have their gun constructed, so they will simply wrench it for the remainder of the stage. They become increasingly paranoid, and soldiers at range tend to fall to snipers. Before worrying about the sentry guns however, it is imperative that the attackers push forward as soon as the first point is taken and establish a foothold close to the second point. See map control for more on the reasoning behind this.
Often the best and sometimes the only way to clear out the defence is an über demoman or heavy charge. If there is a heavy concentration of sentry guns, the übered spearhead may receive so much knockback from the bullets that he becomes ineffective, so make sure you attack from the right angle and take out one gun at a time so they can’t gang up. The demoman rush harrasses the defensive structures, and combining this with an über pyro or heavy rush at the control point tends to freak the defenders out. With their sentry guns down, they have no support when running at the capping attackers so it becomes an even fight, man against man, and an invulnerable heavy or pyro is often all it takes to keep the defenders cowering in fear for a good 5 seconds while the point is taken.
The bottom line here is that sentry guns must go down before any progress can be made. It’s not generally worth even trying to attack while the guns are up. They can occasionally be taken down by an unmarked soldier or demoman, but the most effective method is an übercharged demoman, since a soldier only gets 4 rockets which may not even be enough for 1 sentry if it’s being repaired, whereas the demoman can simply detonate a few sticky bombs at once. Combining this with another rush isn’t necessary but it helps. The important part is that while the demoman is going about his explosive business, the bulk of the attacking team moves in and stands on the control point. Even if the defenders turn up, at least it’s now a level playing field.