Currently, I play songs by learning the tab, but I would like to move more into playing by ear. What is the best way to do this?

Put on a record and play along :D

Seriously, it's a good method, start with easy songs of course. You can also practice with recognising intervals and chords by ear. http://www.earplane.com is a website that comes to mind.

Recognition of intervals and chord(including which inversion if you want) will pretty much give you the ability to play something unknown by ear.

chords no problem. intervals no clue!

chords no problem. intervals no clue!

? ...Intervals should be easy compared to chords.

Listen and play along to as much music as you can. Even different genres than what you normally listen to. Get the TAB or notation and see how it relates to the music being played. Of course, you can also ask questions here. There are a lot of very talented people here that are happy to pass along what they know.

Paul Mac

Pick out tonic notes (key note) from recordings.

Play some improv with musicians who are a good deal better than you (but make sure they know you and will help you out when you really need it) in front of at least a few listeners.

Repeat as often as possible. You'll be using your ears more than ever just to keep up so you don't sound terrible in front of your mini audience. You'll start to remember different clues like the sounds of particular interval changes because you'll need to...sort of like a survival instinct.

The threat of embarrasment can be a great motivator.

If you want to be able to play anything the instant you hear it, you'll find there is no substitue for ear training.

Learn each interval by ear. Find examples to help you remember,such as "Ding -Dong" on many door bells is a major 3rd to the tonic."Happy" to "Birth" in "Happy Birthday" is a major 2nd.In the movie "Wizard of Oz" those flying monkeys sing"wo -ee-o-wee-o" which is tonic on "wo"-perfect 5th on "we", and back to tonic on "o". "Let's ride",the first two notes of the "Flinstones" theme is perfect 5th to tonic.

You can find examples with every song that you can instantly relate to.Put in the time and develope "Big Ears".

Try singing or humming bass parts to help you learn them.
If you're having a hard time doing this, you might have a deeper problem.

If you want to be able to play anything the instant you hear it, you'll find there is no substitue for ear training.

Learn each interval by ear. Find examples to help you remember,such as "Ding -Dong" on many door bells is a major 3rd to the tonic."Happy" to "Birth" in "Happy Birthday" is a major 2nd.In the movie "Wizard of Oz" those flying monkeys sing"wo -ee-o-wee-o" which is tonic on "wo"-perfect 5th on "we", and back to tonic on "o". "Let's ride",the first two notes of the "Flinstones" theme is perfect 5th to tonic.

You can find examples with every song that you can instantaly relate to.Put in the time and develope "Big Ears".
I use different songs to help me...
Minor Second: "Jaws"
Major Second: "Chopsticks" (notes are at the same time)
Minor Third: "Oh Canada"
Major Third: "The Saints Marching"
Perfect Fourth: "Oh Christmas Tree"
Diminished Fifth: just the evil sounding one
Perfect Fifth: "Star Wars Theme Song"
I don't have any for the rest, I'm not that good myself at regonizing the 6s (whether they are major or minor)