For the past year I've been working on and off with S on learning hymns. Now that we are doing our own unofficial "preschool" this year, I'm including a new hymn each week in our curriculum.
Kids in our church start sitting through the service from age three, and I've found that when S knows one of the hymns we are singing, being able to actively participate is a real bright spot for her. She's been in church with us for a year now, and her brother at 2 will be joining us soon enough.
Also, it is so beautiful to hear little children singing great truths. While they may not understand them now, I pray that the words they are memorizing as preschoolers will be a blessing to them someday as adults.
When we are learning a new hymn, I start by singing the first verse to them once. Then I take it one line at a time- singing the tune, enunciating the words as clearly as I can. I try to give a brief explanation of each line so that they have some level of comprehension as to what it is they are singing. If I can think of motions to accompany the words, I will run with it. Whatever helps it to stick!
After going over each stanza of the first verse, I sing it with them a couple of times, encouraging them to sing along as they are able.
From there I will find the hymn on Spotify and/or YouTube. We listen to it in all different styles- being sung by a choir, acapella, guitar, piano, and more contemporary versions. That way they can get it in their heads without mom singing at them constantly, ha ha. I'd hate for my singing to be a nuisance to them ;). It also exposes them to lots of different sounds. I'd love for them to have broad musical exposure and grow up with a taste for variety. I play the hymn while they are playing or coloring, and driving in the car.
I've created a playlist of hymns on Spotify, so each week I add the version most to my taste of the hymn we are learning to that list. This playlist is one we frequently listen to throughout our days, so they are able to review and remember hymns we've learned in the past.
We sing the hymn of the week together at most meals and before bed.
And really, that's about it.
I pick the hymn of the week from the list of what our congregation will be singing next week, so that I know it is something relevant that S can put into practice in church right away. If you'd like to do the same with your own kids, talk with whoever at your church is responsible for music and see if they can give you a heads up on what songs are planned for upcoming Sundays.
Some of my kids favorites that they've learned so far include Trust and Obey; Holy, Holy, Holy; Fairest Lord Jesus; Brethren We Have Met to Worship; and O the Deep, Deep Love of Jesus.
We also work on memorizing Scripture verses and the Catechism... but my philosophy is to pack as much good stuff as possible into them while they are young ;).