extra steps after changing storage engine and adding index
You came to right place. Let's look at an example.

Suppose you have the following MyISAM table:

CREATE TABLE mydb.mytable
(
    id int not null auto_increment,
    firstname varchar(20),
    lastname varchar(20),
    straddr varchar(40),
    city varchar(40),
    state char(2),
    primary key (id)
) ENGINE=MyISAM;


You said you want to do two things:


Change the table to InnoDB
Add an index


For the above table, here is how to convert the table to InnoDB and add an index on names

ALTER TABLE mydb.mytable ENGINE=InnoDB;
ALTER TABLE mydb.mytable ADD INDEX name (lastname,firstname);


Here is a way to make the table InnoDB, index it, and keep the original as MyISAM

CREATE TABLE mydb.mytablenew LIKE mydb.mytable;
ALTER TABLE mydb.mytablenew ENGINE=InnoDB;
ALTER TABLE mydb.mytablenew ADD INDEX name (lastname,firstname);
INSERT INTO mydb.mytablenew SELECT * FROM mydb.mytable;
ALTER TABLE mydb.mytable RENAME mydb.mytableold;
ALTER TABLE mydb.mytablenew RENAME mydb.mytable;


CAVEAT

This answer is really an oversimplification of the conversion. There are still other aspects of setting up InnoDB (Here is a Pictorial Representation of InnoDB's Infrastructure).  Here are a few of my past posts on such configuration due diligence:


Feb 12, 2011 : How do you tune MySQL for a heavy InnoDB workload?
Feb 16, 2011 : How to safely change MySQL innodb variable &#39;innodb_log_file_size&#39;?
Mar 04, 2011 : Clarification on MySQL innodb_flush_method variable
Apr 14, 2011 : What are the main differences between InnoDB and MyISAM?
Sep 12, 2011 : Possible to make MySQL use more than one core?
Feb 22, 2012 : Ibdata usage and Recommendations?
Apr 01, 2012 : Is innodb_file_per_table advisable?