How do I add wireless connection ?

Why such an old release?? Lucid is EOL in 8 months time. Why not install Precise and get support until 2017?

I agree with Anderw you should consider upgarding to Precise.

The first thing you will need is a wireless adaptor of some type. Since your computer is a desktop you probably don't have wireless but we can check that. Open up a terminal (press CTRL+ALT+T) and enter the following commands.

ifconfig; sudo iwlist scan

I see this

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warren@dell:~$ sudo ifconfig
[sudo] password for warren:
eth0 Link encap:Ethernet HWaddr 00:25:64:6d:d3:e3
          UP BROADCAST MULTICAST MTU:1500 Metric:1
          RX packets:0 errors:0 dropped:0 overruns:0 frame:0
          TX packets:0 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:1000
          RX bytes:0 (0.0 B) TX bytes:0 (0.0 B)
          Interrupt:18

eth2 Link encap:Ethernet HWaddr 70:1a:04:69:33:90
          inet addr:192.168.0.2 Bcast:192.168.0.255 Mask:255.255.255.0
          inet6 addr: fe80::721a:4ff:fe69:3390/64 Scope:Link
          UP BROADCAST RUNNING MULTICAST MTU:1500 Metric:1
          RX packets:4103 errors:0 dropped:0 overruns:0 frame:3969
          TX packets:3925 errors:8 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:1000
          RX bytes:3529680 (3.5 MB) TX bytes:625787 (625.7 KB)
          Interrupt:17 Base address:0xc000

lo Link encap:Local Loopback
          inet addr:127.0.0.1 Mask:255.0.0.0
          inet6 addr: ::1/128 Scope:Host
          UP LOOPBACK RUNNING MTU:16436 Metric:1
          RX packets:381 errors:0 dropped:0 overruns:0 frame:0
          TX packets:381 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:0
          RX bytes:69080 (69.0 KB) TX bytes:69080 (69.0 KB)

warren@dell:~$ ifconfig; sudo iwlist scan
eth0 Link encap:Ethernet HWaddr 00:25:64:6d:d3:e3
          UP BROADCAST MULTICAST MTU:1500 Metric:1
          RX packets:0 errors:0 dropped:0 overruns:0 frame:0
          TX packets:0 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:1000
          RX bytes:0 (0.0 B) TX bytes:0 (0.0 B)
          Interrupt:18

eth2 Link encap:Ethernet HWaddr 70:1a:04:69:33:90
          inet addr:192.168.0.2 Bcast:192.168.0.255 Mask:255.255.255.0
          inet6 addr: fe80::721a:4ff:fe69:3390/64 Scope:Link
          UP BROADCAST RUNNING MULTICAST MTU:1500 Metric:1
          RX packets:4109 errors:0 dropped:0 overruns:0 frame:4052
          TX packets:3930 errors:8 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:1000
          RX bytes:3530667 (3.5 MB) TX bytes:626179 (626.1 KB)
          Interrupt:17 Base address:0xc000

lo Link encap:Local Loopback
          inet addr:127.0.0.1 Mask:255.0.0.0
          inet6 addr: ::1/128 Scope:Host
          UP LOOPBACK RUNNING MTU:16436 Metric:1
          RX packets:387 errors:0 dropped:0 overruns:0 frame:0
          TX packets:387 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:0
          RX bytes:69884 (69.8 KB) TX bytes:69884 (69.8 KB)

lo Interface doesn't support scanning.

eth2 Scan completed :
          Cell 01 - Address: 00:0F:B5:50:A8:36
                    ESSID:"1gid46vaylveagu59b3ks232h"
                    Mode:Managed
                    Frequency:2.462 GHz (Channel 11)
                    Quality:5/5 Signal level:-53 dBm Noise level:-92 dBm
                    IE: WPA Version 1
                        Group Cipher : TKIP
                        Pairwise Ciphers (1) : TKIP
                        Authentication Suites (1) : PSK
                    Encryption key:on
                    Bit Rates:1 Mb/s; 2 Mb/s; 5.5 Mb/s; 11 Mb/s; 22 Mb/s
                              6 Mb/s; 9 Mb/s; 12 Mb/s; 18 Mb/s; 24 Mb/s
                              36 Mb/s; 48 Mb/s; 54 Mb/s
          Cell 02 - Address: 1C:AF:F7:63:A5:26
                    ESSID:"TALKTALK-63A526"
                    Mode:Managed
                    Frequency:2.412 GHz (Channel 1)
                    Quality:4/5 Signal level:-61 dBm Noise level:-92 dBm
                    IE: IEEE 802.11i/WPA2 Version 1
                        Group Cipher : TKIP
                        Pairwise Ciphers (2) : TKIP CCMP
                        Authentication Suites (1) : PSK
                    IE: WPA Version 1
                        Group Cipher : TKIP
                        Pairwise Ciphers (2) : TKIP CCMP
                        Authentication Suites (1) : PSK
                    Encryption key:on
                    Bit Rates:1 Mb/s; 2 Mb/s; 5.5 Mb/s; 11 Mb/s; 6 Mb/s
                              9 Mb/s; 12 Mb/s; 18 Mb/s; 24 Mb/s; 36 Mb/s
                              48 Mb/s; 54 Mb/s

eth0 Interface doesn't support scanning.
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I am assuming that you will only see two interfaces lo and eth0 and that neither interface supports scanning. If that's correct you will need to get a wireless interface for your PC Some work well with Linux some dont. Before you spend any money check its going to work first.

Take a look here for some models that have been tested with Ubuntu and are known to work

https://help.ubuntu.com/community/WifiDocs/WirelessCardsSupported

run:

gksudo gedit /etc/udev/rules.d/70-persistent-net.rules

add this line:

SUBSYSTEM=="net", DRIVERS=="?*", ATTR{address}=="70:1a:04:69:33:90", NAME="wlan0"

Save the new file and reboot

HTH (if the 70:1a:04:69:33:90 exists in the file, simply change the line to wlan0)

ACTIONPARSNHIP: Dont know, havent bothered to upgrade but will now.

WARREN; The network connections say Auto Eth0

The modem has wireless also and the green light is on.

The line may help, it will make the device identify as wlan0 which may make it work

@Andrew: the address 70:1a:04:69:33:90 belongs to Warren Hill. He was just giving an example....

Ah...my mistake, sorry