Words are made up of a series of sounds rather than a solid square block of sound. When singing there is all sorts of room to play with the word; movable vowels and consonants. One word (or group of sounds) moves to the next group of sounds continuously.
The longer more expressive sounds are generally vowels. I like to think of the vowels as my “long tube of sound “ which I then shape with my tongue and lips slightly to make the consonant sounds.
To practice, start your first word of a line with its vowel-sound even if the word actually starts with a consonant. This will help you to start with an open throat. Begin by thinking of and shaping your throat with the vowel sound you are about to sing while breathing in. Then sing the first vowel sound, and without stopping that sound, shape the first consonant of the word.
Your sound should be continuous from sound shape to sound shape. The only time the sound will stop is when you take a breath.
aaa-th-aaa “the” aaathaaariiiiveeeerriiisswiiiide (the river is wide)
You can practice whole melodies on one vowel sound to help smooth out all kinds of difficulties. Slide from note to note to help maintain composure and relaxation between pitches.
Next you can practice the song using only the vowel sounds of each word (leaving out the consonants altogether). This takes a bit more work mostly because it is hard to think that way. You can write out the vowel sounds and then sing them (considerably easier). Sing continuously moving from one vowel to the next, only stopping to take breaths.
Try to remember it what this feels like. Change nothing, do nothing.
Add back in the consonants trying to maintain “your tube of sound”. Try not to pinch off “the tube” when you shape the consonants. Merely move your tongue or lips slightly (as little as possible) around the tube. There is no need for facial exaggeration when making consonants.
Check yourself out in the mirror to monitor. Happy tubing!