What type of missions would fighter-bombers like the British typhoon or the American thunderbolt be used for during world war two, did they have specific targets or were they mostly just called in whenever they were needed? What kinds of targets did they usually attack, I know they were used to harass German armoured collumns and logistics but were they also used against infantry or bunkers and the like? How effective were they at performing their tasks?
Speaking of the RAF in particular, it was a mixture. There were "armed recce" patrols roaming around to see what they could find; planned strikes against ammunition dumps and other stationary targets; and close-support strikes flown in support of attacking infantry.
Generally speaking the RAF used Mustang Mk.IIIs for longer-range "armed recce" missions looking for columns of supplies or reinforcements on their way to the front line, and Typhoons for shorter-range interdiction and close-support.
From July 1944 onwards, and particularly during major attacks like Operation Market Garden the RAF maintained a "cab rank" of Typhoons constantly in the air with embedded RAF controllers in leading Army units who could whistle up a Typhoon rocket strike as easily as hailing a cab.
One pilot recalls:
Direct support for the Army was controlled by a VCP [Visual Control Post] with the advancing troops. In our aircraft we carried gridded maps, and an initial indication of the target's location was given by reference to these. When we arrived at the scene the Forward Air Controller would indicate where the rockets were to be placed by firing mortar shells, which gave off coloured smoke, at the target. When organising the attack, you had to take into account the position of the sun, the surface wind and the respective positions of the troops according to the "bomb-line" (i.e. the line between the two armies, which was quite theoretical at times). And you had to be wary of the Germans firing similarly-coloured smoke shells on our boys as soon as our own smoke shells had indicated their target".
Edit: they seem to have been pretty effective - the book cites one example where several formations were vectored in on a Panzer formation in a wood and although the pilots only claimed 3 damaged, the Army found 30 knocked-out tanks when the took the wood, 20 of which had been hit by Typhoon rockets.
Source: "Typhoon Wings of 2nd TAF 1943-45" by Chris Thomas
Osprey Combat Aircraft series No. 86.