Learn the basic structure of the hymn. Most hymns have three to four verses and one chorus. The most common time signatures are 3/4 and 4/4, also known as common time).
Determine the relationship between the melody and the lyrics. Writers often use steps and skips to express emotion of the words. They also use chords that are not in the key of the hymn to add color and/or intensify the message of the song. Some selections will have only words, indicating the singing should be a cappella.
Once you have a good sense of the message to be conveyed and the relationship of the music to it, you can make decisions about dynamics and phrasing and balance. If you are accompanying a chorus, playing all four parts equally is good. Bringing out alto or tenor to assist with harmony at the end of a phrase is OK. For some songs, verses are very introspective, and the chorus is more extroverted in tone. Adjusting dynamics slightly is one way to bring out the difference in the tone of each section.
Be sure to be musical when you play. Getting just slightly softer at the end of each phrase will prevent sounding choppy or clunky. Also, decide when to bring out the bass line. Some movement of the bass line can be rich for color and expression. Bringing out the very bottom for two or three measures is OK as long as you return to the balance once you have adjusted voicing to allow for bringing out color in the music. The same can be said for alto and tenor. If a line stepping up has sharps or flats not found in the key, bringing those out for expression enriches the singing of the choir.
Learn the style of the writer of the songs. There seems to be greater variety of authorship in songs of praise and worship.
Consider what part of the music is to supplement the melody. With songs of praise and worship, there is more inner voicing that does not necessarily function as music for verses. You must learn which music is for singing and which music is for expression.
Once you have learned how to follow writing for verses and for expression, you can decide how to voice the parts. For instance, you would bring out the melody in the right hand and the supporting bass harmony in the left hand. But the inner voices will be a little quieter since they are for background instead of actual expression of the text. Voicing means using more pressure, or more force on one aspect of a musical arrangement than in another.
Be sure to spend time listening to recordings of songs. That will help you learn how to deal with the sheet music arrangement where multiple instruments of original arrangements have been reduced to a piano score. Looking at the piano sheet music while listening is also helpful because you can see the relationship between melody and accompaniment as well as hear it.
If you took some piano lessons but have trouble with reading notes or understanding accidentals, you can get basic music theory books to assist with technical aspects of reading. If you need assistance with balance of sound between right and left hand, or assistance with choosing proper fingerings and hand position, contact a local music association about finding a music teacher.