Thought I'd responded to this but it didn't submit.
The first thing to do is write, write, write and write.
There's the City outlets, including our very own Bluemoon, KOTK & MCIVTA. Once you've got the hang of churning out stuff (and there's a big difference between a 4-500 word piece and a 4-5,000 word one) then a blog is probably the best way, as a friend's son had his blog noticed by the Daily Mail and did some intern work for them. Sadly he's a rag but there are many City blogs. Two of the best are View From A Blue and Down The Kippax Steps. I'm sure the guys behind those will be glad to help you.
There are also some good general websites that welcome writers, such as Bleacher Report and of course, our very own Lucky Toma's Daisy Cutter. In addition, if you're interested, my nephew is Premier League editor of a big international sports website (FTBPro I think it's called) and he would welcome regular contributions on City particularly or the PL in general. I'm happy to put you in touch with him if you want.