Rile42,
From LGA, it's not possible to use only trains to reach Manhattan. If you don't want to take a cab, you must take a bus to the subway. That will cost you 2 bucks, just ask for a transfer on the bus to the subway as it's free.
You can either catch the Q33 bus and ride it to the 74th Street/Roosevelt Avenue terminal or you can catch the Q48 bus and ride it to Flushing. I would suggest the first option, as the bus ride is shorter and you have more subway options at 74th Street.
Assuming that you go that way, at 74th Street go downstairs and catch the
E express train to 34th St/Penn Station which will put you on the west side right near where you want to be.
Now to reach Yankee stadium from that area you've got a few more choices, especially depending on just where you're hotel is located on West 35th Street. If you're close to 6th Avenue, then walk over to 6th Ave and 34th St and catch either a
B or D train. The
D train is preferable, since it run express from 59th St to 125th St.
Please note however, that if you are going between the hours of 3:30 & 8:00 pm Monday thru Friday, the
D train runs express in the Bronx and will not stop at 161st Street/Yankee Stadium. So you would either have to take the
B train all the way or switch at 125th Street from the
D to the
B
If you are closer to 8th Ave, then catch an
A express train at 34th St/Penn Station uptown. Get off at 135th Street and switch to either the
B or D train. Again note the above caution about rush hour
D running express through the Bronx, while the
B is local at all times. Again get off at 161st Street/Yankee Stadium.
You can find subway and bus maps
here to help in your planning.