The overall process to citizenship

Hello again friends!  We're back in the UK and have accomplished getting a phone, car, and flat in our first week!  I'd like to look into moving further along the citizenship trail, so I just wanted to make sure I understood the process correctly.

I have a spousal visa (with a KOL req stamp) that expires 01/01/15 (though i think that could have been a mistake as i was good to enter as of 01/10/12...shouldn't i have received a full three years? ...anyway!).  I must apply for indefinite leave to remain within this time period, right?  Do i have to wait some period of time before I can apply or can I apply now? 

As I understand, citizenship/naturalisation is further down the trail as I have to first live in the UK for three (or five?) years. 

Is that a decent understanding of the process?  any tips?  I'd like to do whatever I need to do know while I have time. 

Thanks again!

Spouse visas are valid for 27 months, and with the KOL endorsement, you can take the Life in the UK test and when you pass, apply for ILR anytime before your visa expires.

Once you have been resident in the UK for 3 years, you can apply for citizenship.

Excellent; thank you, Aquila!