In season 6 episode 1, The Impossible Astronaut, The Doctor cloaks the TARDIS, rendering its external appearance invisible. Is this the first time the TARDIS has shown this capability?
In the old series I remember it actually did blend itself into the surroundings at least a few times. That is confirmed by the main Wikipedia entry on the TARDIS as being in the episodes, 'Attack of the Cybermen' and 'Logopolis'.
It's not the first time, but not by much.
The End of Time, David Tennant's last story, includes the Tardis cloaking.
When The Doctor and Wilfred arrive at Naismiths estate (around 2/3 of the way through part one), the Doctor cloaks the Tardis to stop The Master from finding it.
Update: In light of the comments below, it appears that this isn't an example of acctual cloaking. So, the occasion in The Impossible Astronaut may be the first example after all.
I don't comprehend how this question could go unanswered, or hold an correct answer for such a long span of time:
The TARDIS has been made to be invisible, on one prior occasion: In 'The Invasion' (November, 1968, not to be confused with 'The Invasion (of the Dinosaurs)', from 1974), during which the TARDIS becomes invisible when landing in 1960s London, making difficulty for The Doctor, along with Jamie, and Zoe.
While unintentional, this is a capability that should be easy to replicate at will, as the invisibility is caused by a fault in the 'Visual Stabiliser' (cit 'The Invasion'), and in theory, disabling that component, which is likely linked to the Chameleon Circuit that generates the plasmic shell, would have the same effect.
The subplot of that story, involves building a replacement component, and the serial is a technical sequel to both 'The Web of Fear', and 'The Moonbase'.
In addition, for the record, the Tardis did come with a manual. The Doctor is seen reading from it on more than one occasion when forced (as have other companions, including as I recall, Nyssa, and Adric), tore pages from it in 'The Pirate Planet', spoke of tossing it in a supernova (Matt Smith; because 'he disagreed with it'), used it to prop up equipment, and generally disregarded it.
The TARDIS further has a library record system of computer cards (including 'The Record of Rassilon'), electronic datum systems (but not an electronic manual; however this was faked by the Master in 'Castrovalva'). it is likely that there is also a schematic set, somewhere on-board, but this has never been shown.
Yes, this is the first time the capacity has been seen.
According to a Doctor Who wiki the Doctor's TARDIS has no such ability - it must be either newly added or (less likely) the Doctor aquired a newer model TARDIS.