We are planning to go tomorrow, but are unsure of how to go from Manhattan.We will be coming from around the 30's and Broadway. Any suggestions?

You can take the D train from 34th St/Herald Square to Bedford Pk. Blvd and then bus 25/26 across to the Park. You can also take Metronorth from Grand Central Station. Driving directions are on the NYBG website.
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The most convenient way is to take a Metro North Harlem LIne train from Gr. Central terminal and get off at the Botanical Garden stop. The entrance to thr Garden is a very short walk away. I have no idea as to cost but suspect it will be somewhere around $6 a person if you travel during an off peak hour.

Sorry--I didn't make myself clear. I will be driving. So, now how do I do it?

I copied this from the NYBG website - (I haven't driven in years, I used to live across the street from the NYBG) -
FROM MANHATTAN (East side).
Take the Triborough Bridge (toll) to the Bruckner Expressway (I-278), then NORTH onto the Bronx River Parkway (about 5 miles). Take the Fordham University/Botanical Garden exit (EXIT 7W). At this point the Garden will be on your right and the Zoo on the far left. Bear right, do not go under the bridge. At the traffic light, make a RIGHT turn onto Kazimiroff (Southern) Boulevard (Fordham University will be on your left and the Garden on your right). Follow Kazimiroff (Southern) Boulevard to the Garden's Conservatory Gate on right at 1st traffic light.

FROM MANHATTAN (West side).
Take the West Side Highway and the Henry Hudson Parkway (toll on the bridge) to the Mosholu Parkway (EXIT 24). Follow the Mosholu Parkway to its terminus at the Garden. Turn right on Kazimiroff (Southern) Boulevard. At the third traffic light make a left turn into the Garden's Conservatory Gate.