Joanneg,
First of all find out what school you are in the catchment for and research that one. Depending on where you are, it may be that the school you are in the catchment for is very oversubscribed so that if you live on the edge of the catchment, there is still a possibility you wouldn't get in and so would need to apply to others as well. You will still have to make an application to your catchment school anyway as a formality (application is normally made directly to the school).
Then look at surrounding schools - usually if you want to go to a school that you are not in the catchment for, you make an application to the LEA, NOT the school (check this though as it may vary by LEA).
Normally you have to apply by the March/April of the year your child will start reception (obviously the year before if you want to go to pre-school nursery) - but again, check this as it may vary by LEA.
To get a vague idea of standards of the schools look on the bbc website for school league tables. You can put in your borough and look at the overall results and where each school 'ranks' compared to others in the LEA and the national average. I know some people hate league tables but it's just away of getting an overview of standard of results. Also you can look at Ofsted reports - Ofsted have their own website but I think you can get to it via the BBC one.
I would be looking at other things too (getting A* in everything is not the be all and end all - for me, the key is that my kids are happy at school!). You'll get a feel for the school and staff when you look round - look for things that others have mentioned on here. Also, what is the whole ethos of the school and it does it sit with what you want from a school? My ds will go to the catchment area school but I'm lucky it's one of the top in the LEA but the things I like about it (other than things mentioned below) are that it has loads of good extracurricular activities, it's great on sport and is affiliated to the local healthclub that we are members of so they do lacrosse there and hockey. They have chess, good language clubs etc. The school is very well maintained and they have a HUGE playing field, huge playground. They've got fab IT facilities and library. Also, they cook the school meals on-site which I like - lots of school have them brought in.
With regard to the 11+, I don't know about your area but I know there are very few now that have state grammar schools and the 11+ (we're in Trafford and we still have it), so you need to look into that.
It's hard to know what questions to ask but unless there is something very specific you want from a school, or something that really bothers you, just go along and the questions will probably arise as you go round. Also, like others have said, you really do get a feel for whether it's a nice school or not.
HTH!