Okay, where you may be getting confused is that it's not called a spousal visa if you're applying from within the UK... what you will actually be applying for is an FLR(M) extension visa (Further Leave to Remain).
A spousal visa can only be applied for from outside the UK if you are already married before you move. It is valid 33 months and costs £1,195 + £600 IHS surcharge = £1,795 in total.
An FLR(M) visa can only be applied for from within the UK if you get married on a fiance visa (or you get married while living in the UK on a work or student visa). It is valid for 30 months and costs £811 + £500 IHS surcharge = £1,311 in total.
However, the visa fees will be rising next month, so it will be a bit more than this when you apply.
The FLR(M) application is basically the same as the fiance visa in terms of documents you need, except this time you include your marriage certificate instead of evidence of plans to marry. So, you need updated accommodation and financial requirement documents.
Also, instead of your relationship evidence showing visits and communication while apart, you are supposed to include 6 pieces of mail addressed to both of you (either jointly or individually) at the same UK address, evenly spread over the time you've lived together. However, if you have only recently moved and don't have mail in your name yet, then you can explain this on the application.
You can either apply by post, mailing your documents off to UKVI after you are married, but this can take up to 2 months to be processed, or you can pay an extra £500 (or could be more when the fee rise in April) for an in-person appointment - which will give a same-day decision and then your BRP card (visa) will be mailed within 10 working days.
See here for more information about applying for FLR(M):https://www.gov.uk/remain-in-uk-family/overview
The application form is here:https://www.gov.uk/government/publications/application-to-extend-stay-in-the-uk-as-a-partner-form-flrm