Getting Processor Information

To get the Processor model use the below command in a terminal.

cat /proc/cpuinfo  | grep 'name'| uniq

To get the information about number of processors

cat /proc/cpuinfo  | grep process| wc -l

The simplest way to do this is to use the command created for that, lscpu:

user@host:~$ lscpu
Architecture:          x86_64
CPU op-mode(s):        32-bit, 64-bit
Byte Order:            Little Endian
CPU(s):                2
On-line CPU(s) list:   0,1
Thread(s) per core:    1
Core(s) per socket:    2
Socket(s):             1
NUMA node(s):          1
Vendor ID:             GenuineIntel
CPU family:            6
Model:                 55
Model name:            Intel(R) Celeron(R) CPU  N2840  @ 2.16GHz
Stepping:              8
CPU MHz:               697.301
CPU max MHz:           2582,3000
CPU min MHz:           499,8000
BogoMIPS:              4331.60
Virtualization:        VT-x
L1d cache:             24K
L1i cache:             32K
L2 cache:              1024K
NUMA node0 CPU(s):     0,1
Flags:                 fpu vme de pse tsc msr pae mce cx8 apic sep
mtrr pge mca cmov pat pse36 clflush dts acpi mmx fxsr sse sse2 ss ht tm
pbe syscall nx rdtscp lm constant_tsc arch_perfmon pebs bts rep_good nopl 
xtopology nonstop_tsc aperfmperf eagerfpu pni pclmulqdq dtes64 monitor 
ds_cpl vmx est tm2 ssse3 cx16 xtpr pdcm sse4_1 sse4_2 movbe popcnt  
tsc_deadline_timer rdrand lahf_lm 3dnowprefetch epb tpr_shadow vnmi 
flexpriority ept vpid tsc_adjust smep erms dtherm ida arat

This command will tell you your chipset's characteristics as well as any supported instructions (or flags) in an easy-to-use and simple-to-read manner.

It's often overlooked, so worth a shot. Sorry if this is insultingly obvious :

Alt-F2, then gnome-system-monitor

Also, when I ran sudo lshw | grep -i cpu, I see a line which says cpus=2.

In ubuntu 14.04 desktop, the system monitor tool no longer has a "System" tab. You should see roughly the same screen like this:

1. click the settings wheel (to clarify: the taskbar icon in the absolute upper-right hand corner of the screen: )
2. choose "About this Computer"

You can just use this : more /proc/cpuinfo in your command line.

Then you faced with something like this :

You can use this for more information :

The Hardware Lister application (lshw-gtk) from the default Ubuntu repositories is a user-friendly GUI application that displays detailed information about your computer's hardware including the model name and architecture (32-bit or 64-bit) of the CPU.

Simply select a category to obtain detailed information about a hardware component from the main interface.

Use the uname -m or arch command from the terminal.

For a 64-bit processor and kernel, the command will output x86_64.

The simplest way is from Launcher select System Settings-->Details:

This identifies both your CPU model number and whether 32-bit or 64-bit software is running. It also displays other useful information such as amount of RAM.

Now take your CPU model number in google search engine type 3630QM number of cores:

Replace 3630QM with the model number you get from the first display.

All the other answers are great answers but if you really want the "simplest" way of doing this I believe this is the preferred method without opening a terminal session or installing new software.