I believe the PS3 patch has already been released, with the XBox 360 one to follow shortly.

Official announcement

Single Player
• Resolved a gating issue in “Cliffside Bunker” caused when the hanging cargo on the stern of the Endurance does not react to your bow rope
• Fixed a second issue in “Cliffside Bunker” where you were unable to pull the hanging cargo due to a missing gear item awarded after the melee fight
• Addressed a rare traversal issue in ”Shipwreck Beach” (nighttime) where the second gondola was missing after a checkpoint
• Fixed infrequent issue that caused enemies to disappear when hit with a shotgun, occasionally gating progress
• Addressed uncommon gating issues during the ”Chasm Monastery’s” bridge onslaught where players are unable to progress past the wooden barrier
• Prevented the rare possibility of receiving credit for a collectible in ”Research Base” more than once
• Fixed issue which would occasionally cause infinite loading when fast traveling
• Fixed issue where ”Shipwreck Beach” would not load properly after saving and quitting near an optional tomb, causing players to fall through the world
• Fixed a rare issue where the Cinematic in “Solarii Stronghold” would not start
• Addressed a rare issue in ”Coastal Forest” where the world wouldn’t load after opening the Ancient Gate
• Addressed an issue in ”Shipwreck Beach” where the mast on the wooden ship was occasionally missing depending on the player’s path
• Resolved a gating bug in “Base Exterior” where you are unable to return via fast travel back to the Radio Tower Basecamp
• Fixed a gating issue in “Research Bunker” where the elevator would get stuck in an unintended state
• Resolved an occasional issue where large opponents would appear invincible despite the reticule changing color to red
• Prevented players in “Shipwreck Beach” from pulling the life raft over to an axe climb rock causing them to confuse the world and unable to progress the story
• Minor updates to localized fonts
• Updated Lara’s injuries later in the game to be more consistent in and out of cinematics
• Improved stability of UI

Multiplayer
• Fixed occasional crash when signing out from the multiplayer loading screen
• Addressed crash that occasionally occurred by leaving the game before the loading screen appeared
• Improvements to multiplayer match stability
• Fixed issue where canceling a title update after selecting multiplayer/Square Enix in the Main Menu results in locking out the controls
• Addressed rare crashes entering multiplayer game in progress
• Fixed bug where a user’s body would shrink if killed by death plane, electric pole, spike trap, or fire, in certain circumstances
• Improved stability of host migration during a match
• Addressed an issue where players could die with a super weapon and respawn still in possession of it
• Fixed bug with Assault Rifle tracers
• Fixed an issue where being shot with the Power Bow while jumping onto a flagpole causes the player character to become stuck in a grabbing animation
• Addressed traversal issues in “Shanty Town” map that allowed players to fall through the map
• Resolved grenades not attaching to players or exploding properly
• Addressed issues where throwable weapon triggers incorrect SFX
• Fixed voice over issues at the start of a match
• Addressed animation glitches when reviving other players
• Fixed bug where players could get stuck when walking up a slope with a Medkit

A new patch has been released for XBox 360, with a PS3 version to follow later.

Patch Notes:

Single Player

• Resolved situation in which combat would not spawn the next encounter on Chasm Bridge, halting player progress.
• Fixed an issue in Shipwreck Beach where if a player skipped content they would be unable to progress due to not receiving the compound bow from Jonah. This was known as the “Block & Tackle” bug. The update should address this issue for players who have already encountered the bug. Fixed a similar issue where the block and tackle itself was inaccessible while on the galleon.
• Resolved issue where players were able to proceed through Shipwreck beach without the compound bow.
• Addressed issues with visibility and movement of sea mines in Shipwreck Beach.
• Addressed issue where skipped cinematics were preventing saving your discovery of the next campsite in Mountain Base (Radio Tower Basecamp) and Chasm Monastery (Sacred Hall Basecamp).

• Resolved issue with fire arrows blocking progress in the Tomb of Lost Adventurer.
• Fixed issue in Coastal Forest where reloading last checkpoint generated an incorrect objective.
• Resolved a rare issue in Shantytown where the player path could be gated following a combat encounter.
• Addressed a situation while re-traversing the Cliffside Bunker where the world would not load as you exited the roof.
• Fixed rare case where gondolas would drop prematurely in Shipwreck Beach making traversal difficult.
• Resolved issue in Tomb of the Unworthy where basecamp discovery notification would play at the incorrect time.
• Fixed crash that occurred only on Korean Language.
• Addressed visibility issue when toggling Square Enix Trailers on PS3.
• Polished timing of Czech subtitles.

Multiplayer

• Improved how Lobbies handle users with Downloadable Content/Additional Content maps, allowing friends to play together.
• Implemented additional Downloadable Content/Additional Content matchmaking options menu.
• Added notifications for Downloadable Content/Additional Content matchmaking options.
• Addressed an issue where a black screen would appear after accepting a friend invite and removing the Ethernet Cable.
• Fixed a rare multiplayer crash.
• Addressed an issue with empty text characters not displaying on PC and PS3.
• Adjust unit of measurement for time played in Online Profiles.
• Added an option to search All game types in matchmaking.
• Resolved an occasional issue where Salvage Crates wouldn’t respawn after Host Migration.
• Retuned Shopaholic Achievement by excluding The Oni General from the achievement requirement.

Now that's what I call a laundry list lol ... Thanks!

So how would you install the XBOX 360 patch on it?

Do you need to have an XBOX 360 Live account and card with valid minutes on it?

Xbox offers you an update when available when you launch the game.

Xbox offers you an update when available when you launch the game.

It didn't do it and of course, I don't have an Xbox live account

ah maybe that's why and it needs an internet connection.

I don't have an Xbox so I'm not entirely sure, but I believe that you can download patches and DLC with a free Xbox Live account, so you wouldn't need to pay for a Gold account to update your game.