OK, she is an EEA Citizen, so doesn't need one, but you are not, so need to apply for a CoA ... Certificate of Approval to Marry ... application now free .... and having got that CoA the two of you will be permitted to get married in the UK. Take a look at
this UKBA webpage.
When are the two of you intending to get married?
Following the marriage you will be a "family member" of an EEA Citizen, and thus will be permitted to apply for a Residence Card, using application form EEA2, and this will confirm that you also will have Treaty Rights, including the ability to live in the UK, and to work, study, etc..