How to load iwlwifi driver?

You can load the driver with:

sudo modprobe iwlwifi

The driver iwlwifi and, indeed, the required firmware are included by default in all recent Ubuntu versions. If it is not loaded, something else is wrong.

Is yours really an iwlwifi device? Check:

lspci -nnk | grep 0280 -A3

Is the switch or key combination set to enable or disable the wireless? Check:

rfkill list all

Are there any clues in the log?

dmesg | grep iwl

After we find out more, I will edit this question to add additional troubleshooting steps.

The absolutely simplest way is to reboot. This ensures that all modules are loaded cleanly, on boot.

The other alternative is to manually remove it:

sudo modprobe -r iwlwifi

and reinsert it it

sudo modprobe iwlwifi

But iwlwifi typically has a couple of modules that depends on it, so it may be easier to reboot, if sudo modprobe -r iwlwifi returns any errors.

To see dependencies, run lsmod | grep iwl

[~]$ lsmod | grep iwl
iwlmvm                364544  0 
mac80211              782336  1 iwlmvm
iwlwifi               180224  1 iwlmvm
cfg80211              610304  3 iwlwifi,mac80211,iwlmvm
[~]$ 

In this case iwlmvm depends on iwlwifi, so it has to be removed as well.