How to upgrade Linux kernel to Debian Jessie?

I want to install docker but when I run the daemon it complains that the kernel is too old.
Your Linux kernel version 3.2.0-4-amd64 is not supported for running docker. Please upgrade your kernel to 3.10.0 or newer.

Look current version:
uname-r
3.2.0-4-amd64

I want to upgrade to 3.16.0-6 (the latest LTS version available for addition to the repository of Debian wheezy).

Do:
apt-get install linux-image-3.16.0-6-amd64 linux-headers-3.16.0-6-amd64

The output of uname-r is the same.

Questions:
1. How to update the kernel version that uname-r gave another number?
2. Does it make sense to use ukuu?
3. How best to act to less to break during updates?

UPDATE

Source on the same machine had two systems, both Debian 8, differed only in minor versions. About the second system are forgotten as not used it due to the fact that it was not working Wi-Fi.

On advice I updated grub, which was on the topic of the second system:
update-grub /path/to/root/second/system/boot/grub/grub.cfg

Grube then came the launch of the first system with the new kernel.

After starting the main system from the new kernel booted successfully, visually the logs looked the same.
Wi-Fi stopped working.
Checked the second system the original used a more recent kernel.
I have no idea why the driver wifi adapter or something is not working with the new kernel, but the regularity is obvious.
Now booted with old kernel, no problem.
March 19th 20 at 10:30
2 answers
March 19th 20 at 10:32
Solution
Installation is not enough. Still need to reboot into the new kernel. This should be generated appropriate keys for grub, but this usually happens automatically.

2. No
3. If this is the only machine and no specific services like nfs, ceph, iscsi, - no, the probability to break something minimal. If you're doing the smart thing, then you need to do a clone car and try it as a "sandbox" update
updated the details in the question.
As it turned out, breaks Wi-Fi. - alexanne commented on March 19th 20 at 10:35
Well, then look for a suitable version of the wifi drivers. In Debian, unlike Ubuntu, this is sensitive more difficult, because their policy is not to include anything proprietary in the distribution. But, I'm sure the problem is solved very quickly.
By the way, I thought somehow that it is about the server, not the desktop. - Domenica.Halvorson commented on March 19th 20 at 10:38
March 19th 20 at 10:34
And you rebooted after installing the new kernel?
Yes - alexanne commented on March 19th 20 at 10:37
@alexanne, load a new kernel. If it's not on the menu, then update your Grub config. - Nadia.Co commented on March 19th 20 at 10:40
Updated the grub, I added the details to the topic. - alexanne commented on March 19th 20 at 10:43

Find more questions by tags DebianLinux