How can I get to dobbs ferry from manhattan with public transportation?

It is very easy to use Metro-North Railroad. Metro-North is not only option, there are also slow option via Bee-Line Buses.

Via MetroNorth
Take (F)(D) or Weekday (B) to 42nd St-Bryant Park.
Transfer to Queens-bound (7) one stop to Grand Central.
Exit station and follow sign to Metro-North Railroad.
Before you board Metro-North Railroad, don't buy ticket onboard because onboard purchases are expensive.

Here is video guide how to use Long Island Railroad/Metro-North Railroad Ticket Vending Machine.
http://www.youtube.com/s89hblr#p/u/26/Az...
For Metro-North TVM, you follow option. Instead of Penn Station to Another Station, it will say Grand Central.
Choose D for Dobbs Ferrry. Fare will be Peak $9.75 and off-peak $7.25.
Your train will be called Harlem Line. Listen carefully to announcement or see departure info.
Take Harlem Line to Dobbs Ferry. Most trains stop there are local.

Via Bee-Line Bus Option.- Same fare as NYC Subway and Buses.
You could take (D) or weekday (B) to 59th St.
Take (A) to 168th St.
Take (1) to 242nd St.
Transfer to Bee-Line #1 bus to Dobbs Ferry.
From (F), take to 6th Av station at Broadway-Lafayette, West 4th, 34, 42nd or 47th-50th Sts for (B)(D) to 59th St. At West 4th, 59th Sts, transfer to (A) to 168th St for (1) to 242nd St for Bee-Line #1 bus.

This Site Might Help You.

RE:
How can I get to dobbs ferry from manhattan with public transportation?
I live near the F, B, and D trains. (MTA)
I also have no idea how to use the metro north, details on that would be helpful.