There are two types of beginners, those who have played other instruments such as guitar or piano or have studied voice and those who are new to all types of music except for singing in the car etc. There is a vast difference between the two groups but the first step is to get a ukulele. The most common size is the soprano but if you have large hands you might want to get the concert size which is a little larger. You will also need and electronic tuner and a book of chord diagrams for ukulele tuned in the key of C; GCEA. Most likely if you are reading this you already have experience with some other instrument and are wanting something simple and portable. The ukulele is small and has only four strings but this also describes a violin and the ukulele is every bit as sophisticated and versatile as the violin and much easier to play. In the 20's and 30's when the ukulele was most popular, the best American poplular song writers and composers were at their peak and the ukulele was the most common instrument, being best suited for the jazzy tunes of that era.
Many of the songs you want to play will probably be in a key that is too high or too low for your vocal range. If so you can tune your ukulele up or down one note and if this doesn't get low enough, get a tenor uke which is tuned D G B E and use a capo to raise the pitch to the proper key for your voice range. A capo is a small bar that straps around the neck and holds all the strings down on the same fret. The original sheet-music arrangements were usually pitched for a female vocalist who would sing with the band.
Start off playing and singing easy songs such as those in the Jim Beloff Camp songbook which has diagrams showing where you put your fingers to make the chords. If you know someone who plays the ukulele or guitar get them to show you how to hold your fingers. A ukulele is tuned like a guitar with a capo on the 5th fret and the lowest two strings removed except that the 4th string is an octave lower on the guitar. Ukuleles can be tweaked by making the grooves in the nut lower so you don't have to press so hard to hold the strings down. Use a fine hacksaw blade and not a knife to do this, and if your uke is valuable or expensive get a professional to do this for you. There are lots of free instruction videos on youtube.com and other sites you can watch. Learn the basic chords: C F G7 in the key of C and F Bb C7 in the key of F and you will be able to play most country and folk songs. The main bluegrass chords are G C and A for playing in the key of G, the key used by a lot of bluegrass music. Here is an internet site with chord diagrams: ukulelesongs.com.
If your ukulele is rare, fancy or expensive you will not want to leave it out of its case. If that is your situation, you should buy a cheap, beat up playable ukulele that you can leave out in view (but not in a chair or on the bed) all the time. This way you will pick up the uke and play it constantly which is how you learn. If the TV sound is distracting, turn off the sound and just watch the picture while you practice.
If you are new to music you will have to learn to sing in the same key that you playing on the uke. If some of the notes are too high or too low for you to hit, use a capo to raise the key or tune the uke to a lower key such as Bb with the ukulele tuned F Bb D G. At first you should play songs you have heard over and over. If the music doesn't have ukulele chord diagrams, draw them in yourself, preferably in pencil. This will help you learn the chords by their names.
There are certain songs that work well on the ukulele, and others that don't. The best are from Tin Pan Alley in the 20's and 30's but many of them are a little tricky. Some of the folk songs from the sixties are easier to play and still are entertaining.
The Wheels On The Bus ukulele chords
This song has only two chords: F and C7, which are shown above. The song starts with the F chord and then changes to C7 on the second repitition of "round and round" and then changes back to F on the third iteration of "round and round" and then the pattern repeats. Strum your uke by using your index or middle finger strumming down with your fingernail and up with the ball of the finger.
Four Chord Songs: "Blue Moon", "Heart and Soul" ukulele chords
Many popular songs such as "Heart and Soul" and "Blue Moon" can be played with four chords which are played in a sequence that repeats over and over (except for the bridge, the middle part). In the key of F the chords are F Dm Bb and C7. Gm7 can usually be substituted for Bb and is easier to play. You can look at the diagrams above or copy the chord diagrams from ukulelesongs.com and practice them a while before you start singing. In the key of C, the key that is used for "Heart and Soul" on the piano, the chords are C Am F and G7. Many of the doo wop songs can be played with these same chords such as "Goodnight Sweetheart Goodnight". The complete chords to these songs can be usually found on the internet by searching under the name of the song followed by the word "chords", but beware a lot of the time the chords on the internet are not right. Try several sites and versions.
Three Chord Songs
Thousands of songs can be played with just three chords. In the key of F the chords are F, Bb and C7. In the key of C, the peoples's key, (according to Ian Whitcomb) the chords are C, F and G7 and in the key of G, the most common key for bluegrass players, the chords are G, C and D or D7 depending on your taste. It sounds more like bluegrass with the D chord. If you need to play along with a guitar player playing in the key of E, you can tune you uke to the key of B, one half step down, and play F key chords but they will actually be the chords in the key of E.
Most folk songs and most country songs can be played with these chords. Try the "Sloop John B" in F where the chords are F, the C7, then back to F, then Bb, then F then C7 and end on F. Try the chords and you will probably be able to tell when to change the chords. If the pitch is too low, play the same sequence of chords in the key of G.
Country Ukulele Songs: "Honky Tonk Angel" ukulele chords
The classic country songs can usually played with the three cords shown above, but sometimes you can play the 7th of the main chord as a transition to the usual second chord thus: C, C7, F, G7 and back to C. Listen to "Your Cheatin' Heart" for that effect. And here is yours truly playing "Honky Tonk Angel" with a country band with the uke tuned in the key of B so that I can play the chord forms for F and yet be in the key of E which is the key the band is playing in. (The bridge of "Cheatin' Heart" in the key of C requires that you play a D7 chord starting at the word "round", so in the bridge the chords are F, C D7 G7).
When the great American songwriters were young, their main source of income was from sales of sheet music. Now sheet music sales are falling and many great songs are out of print. Therefore, if people give you old sheet music take it and keep it. If you go to estate sales look inside the piano bench and make a low offer for what's inside. Sheet music from the twenties and thirties usually has ukulele chord diagrams instead of guitar chord diagrams and you can usually find video clips of the songs on youtube.com and other internet sites.
Its pretty easy to pick out the chords by ear when you are playing three-chord songs, but the great Tin-Pan-Alley songs are another story. Try "After You've Gone" the sheet music to which is shown on this website. Even people who have played it many times can't always remember the chords and so use the sheet music. Though the great songs are harder they don't get boring even when you practice them over and over and this is one reason they still are played: the musicians like to play them for their own amusement.
As you become able to strum your uke and change chords rapidly, you will want something less boring than the common three and four chord songs commonly heard today. You will then need the sheet music because the great songs for uke have lots of unusual chords you will never be able to figure out by ear. Sheet music at the present time seems to be hard to find and is often out of print, but if you let people know that you're looking for it you will have people wanting to give or sell you large collrctions. My advice is that you take the music collection because it will become worth more than you ukuleles now that individual songs cost five to ten dollars even on ebay.com. My book the Ukulele Players Guide has lists of some of the best songs (and records) that you should look for.