If you are just looking for text messaging through Skype, their
recently released software for Symbian (Symbian is the operating software used by most Nokia handsets) will do it, however not on the E61, as it's outdated and not supported.
Fortunately there's an alternative free software called
Fring, which supports not only the E61, but nearly every instant messaging service (including Skype) and VoIP at once. So just download Fring to your handset, sign up for Fring and then configure all the IM and VoIP-accounts you want to use.
However since the E61 does neither support HSUPA nor HSDPA you are likely to experience inferior sound quality and a bit of a lag while talking via VoIP.
Btw, the E61 has also an integrated VoIP-client by default, which is very comfortable to use, as it's highly integrated. After dialing a number or picking one from your phonebook you can simply go to Options / Internet call and the call will be placed via VoIP. No need to start any application etc. Of course you need to configure a VoIP-account before.
P.S.:
Here 3 UK offer their Skype client for download, however there's no version for the E61 either - so Fring is your only choice.