The cement in this wall was weak as it probably didn't get enough cement in the mix. When the wall was leant on some of it fell down.
Take out the loose bricks all around it and clean up all the bricks on and off the wall
Use eye protection while chipping out the cement.
Use a light claw hammer and a small scutch chisel to remove the old cement.
A heavy bloster may break the bricks, light taps are what you need.
Clean off the old mortar so you end up looking like this.
Clean up your mess and set aside.....
Mix your sand and cement to 4 parts sand to 1 part cement.

Don't make the mix too sloppy.
A sloppy mix and a beginner is a sure recipe for disaster.
Slightly dry is better that slightly wet.

Getting the mix at the right consistency will make your job much easier.
Too dry and it will be hard to spread evenly, too wet and your bricks will end up stained and it will be difficult to lay the bricks at the correctly.
Remember that drier is tidier.
Now we look like this.
The soldier course on this wall will be a bit tricky for a beginner but I'll show you how I do it.
First lay a small amount of cement.
The reason for only laying a small amount at a time is that if you don't you might find it drying up.
Soldier courses take a bit of time to get right.
Fill the "frog" or the indent in the brick with cement and then add cement round the 3 edges of the brick.
Place the bricks and gently tap into position ensuring the tops and sides align.
This wall was not level so the use of a spirit level is only good for aligning, not leveling.
The first one should look like this.
When you have 5 or 6 bricks left to go, you need to mark their  
position so you know where to place them.
When you get to the last one, add cement to the brick on the wall also.
You will not get a perfect bed but you can fill it later.
Nearly there now...
There is an iron in tool meant to do this job but I normally use a piece of hose pipe.
Now it looks like this.
A dry paintbrush will remove the loose cement and smooth the joints.
Job done!!!

Of course if you don't want to try it yourself you can always call BBS for an estimate (subject to your area that is).
How to repair a brick wall
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