The early 1960s were a revolutionary time for music. The style was a mixture of leftover 50s influence, British rock and roll, and various genres, such as doo wop and rhythm and blues. Anyone who has attempted to write a "She Loves You" style Beatles song has probably attempted to write in this style.
Unless you're going for a modern crossover, it's best to keep the lyrics clean and earnest, and at most hint at things (Please Please Me). It may sound a bit cliched, but that's sort of the idea. Early 60s songs exuded a very playful innocence that can be surprisingly difficult to recreate. A good rule to keep in mind, use pronouns, and use them often.
Make good use of transitional chords. Make a major chord a seven when going to the bridge, go from a major to its minor (ex. A to Am) to build up to the high point of the song. Consider blues chords and rhythm for rock and roll style songs. For uptempo songs, a good thing to try would be to sing the opening lyrics a capella, and then come in with the melody. This occurs in songs like A Little Loving by the Fourmost.
The chorus has been a mainstay of music for quite some time, but it wasn't always that way. In the early 60s, most songs used a refrain instead. A refrain is similar to a chorus, however, rather than being a separate section of the song, a refrain is more like an extension of the verse. Therefore, where in modern music, we would expect something like
or ABABCB, a 60s song would be more likely to do
or AABA. Because by the Dave Clark Five is a good example of this structure. The DC5 actually tweak the structure a bit, the bridge comes before the second verse. If anything, this shows that there is no one set in stone structure, but AABA is a good place to start. Because also has another section common in 60s songs, a solo. The solo usually comes after the bridge, but it can occur in other places, and there may not be a need for a solo at all.
Early 60s songs generally run between 1:30 and 2:30, a very short amount of time by our modern standards. Yet despite that, they managed to fit a lot into that time frame. Besides verses, refrains and solos, the bridge was often played twice and sometimes even three times. Treat the bridge as an equal to the verses rather than a one-off, especially if you are going to be repeating it. It should feel like a natural part of the song. An option to consider would be changing the bridge's lyrics on the second go around to keep it fresh. It can be challenging to keep a song short yet still imbue it with meaning, but with the right lyrics and melody, it can be done to fantastic effect.
6. Vocals and instruments
Use harmonies, lots of harmonies. You can't have too many. Some groups like the Beatles sang in duet or three part harmony throughout in many of their early hits, whilst others had harmony in the verses, refrain or bridge. If you happen to be good enough to harmonize with yourself, that is always an option. Otherwise, try to find some collaborators. Instrumentally, keep it simple. Guitar is going to be the centerpiece, rhythm and (if necessary) lead. If you are talented at multiple instruments or are part of a group, add bass and drums. Less common but still acceptable are the piano, organ and saxophone.
Bonus - Write another, release on Vinyl
If the opportunity should arise and you happen to have written another 60s song, you might decide to be very authentic and make them the A and B sides of a vinyl single.
This is by no means a comprehensive guide, and it's probably not even a good one. But if anyone gets anything good out of this, even just the idea to go and find someone who explains it better, I'll feel like it was worth writing. I love 60s music and would like to help keep it alive any way I can. So that's it, thank you for reading, and good luck, the toppermost of the poppermost awaits.