Q:

is index still effective after data has been selected?

I have two tables that I want to join, they both have index on the column I am trying to join.
QUERY 1
SELECT * FROM [A] INNER JOIN [B] ON [A].F = [B].F;

QUERY 2
SELECT * FROM (SELECT * FROM [A]) [A1] INNER JOIN (SELECT * FROM B) [B1] ON [A1].F=[B1].F

the first query clearly will utilize the index, what about the second one?
after the two select statements in the brackets are executed, then join would occur, but my guess is the index wouldn't help to speed up the query because it is pretty much a new table..

A:

The query isn't executed quite so literally as you suggest, where the inner queries are executed first and then their results are combined with the outer query. The optimizer will take your query and will look at many possible ways to get your data through various join orders, index usages, etc. etc. and come up with a plan that it feels is optimal enough. 
If you execute both queries and look at their respective execution plans, I think you will find that they use the exact same one.
Here's a simple example of the same concept. I created my schema as so:
CREATE TABLE A (id int, value int)
CREATE TABLE B (id int, value int)

INSERT INTO A (id, value)
VALUES (1,900),(2,800),(3,700),(4,600)

INSERT INTO B (id, value)
VALUES (2,800),(3,700),(4,600),(5,500)

CREATE CLUSTERED INDEX IX_A ON A (id)
CREATE CLUSTERED INDEX IX_B ON B (id)

And ran queries like the ones you provided. 
SELECT * FROM A INNER JOIN B ON A.id = B.id 
SELECT * FROM (SELECT * FROM A) A1 INNER JOIN (SELECT * FROM B) B1 ON A1.id = B1.id 

The plans that were generated looked like this:

Which, as you can see, both utilize the index.

A:

Chances are high that the SQL Server Query Optimizer will be able to detect that Query 2 is in fact the same as Query 1 and use the same indexed approach.
Whether this happens depends on a lot of factors: your table design, your table statistics, the complexity of your query, etc. If you want to know for certain, let SQL Server Query Analyzer show you the execution plan. Here are some links to help you get started:

Displaying Graphical Execution Plans
Examining Query Execution Plans

