Honestly, in my experience, the easiest and most cost-effective way from LaGuardia (or Newark) into Midtown is to take the New York Airport Service Express Bus. It runs from the lower-level baggage claim at the LaGuardia terminals and goes to Grand Central, Port Authority, and Penn, in that order.
When you get outside security and claim your bags (if you checked any), just proceed out to the curb and look for the huge signs (usually red, white and blue) that say something to the effect of 'Express Bus to Manhattan' or 'New York Airport Shuttle,' etc. If in doubt, just ask someone - everyone knows what those buses are.
If you are going to Times Sq area of Broadway (which is my guess), then your best bet is probably to get off at Grand Central, as it is the first stop, and thus avoid the midtown traffic. From there, hop a cab over to Broadway (5 blocks west) or you can also get the S (shuttle) subway line and just go one stop to Times Sq-42nd St.
The bus runs about every 25-30 minutes, and the ride - at that time of the morning - shouldn't be more than 30 minutes into midtown (barring a wreck or something which could be par for the course on the BQE at any time of day).
The whole thing is actually pretty easy, and not to tiring. However, if none of this sounds to appealing to you, or you are going to be with a few other people, than it might well just pay to take a taxi from LaGuardia right into Midtown, which at that time shouldn't (theoretically) take more than 20-30 minutes, and cost probably somewhere in the neighborhood of $35-45.