1. Take singing seriously
This is my number one bugbear; people saying, "Oh, you're so lucky you can sing!" as if years of singing lessons and practice have nothing to do with it. Yes, people have a greater or lesser amount of natural talent, but there is a LOT of craft to learn with singing too. Take time to learn the craft from an expert teacher. Practice.
If you can't do a really good job of singing and playing an instrument at the same time then pick one to focus on. I think it's not good enough for a lead singer to be a great guitar player and a slap-dash vocalist. (Of course there are many highly successful examples of exactly that, but it irritates me a little).
Elton John is a brilliant example of someone who can sing beautifully while playing an instrument.
Learn the songs until you are 100% of where every note is and what it takes to get there. Don't scoop up to (or just under) high notes. Don't meander vaguely around the notes thinking you're being all R n B. Pick (or write) songs in a comfortable range so you're not straining to hit notes that are either too high or too low.
As documented, I love Franz Ferdinand with big love, but Alex gives a great (or not so great) example of scooping up to just under the note around 3:49 when they go into "I feel love" in this clip.
3. Give notes their full value
You don't need to sing long notes all the time, but stop somewhere logical i.e. at the end of a bar. Don't just trail off vaguely 'cos you can be bothered or you're running out of breath.
4. Think about when to breathe
Generally, don't breathe in the middle of a phrase. PLEASE don't breath in the middle of a word! A breath is like a pause in the flow of ideas; it can highlight something or switch up the rhythm. Practice and good technique can give you enough breath to deliver thoughtful musical phrases as you sing. Adele has interesting phrasing and impressive breath control in this song, especially in the chorus around 1:26 when she carries on over first line into the second line to keep the energy going.
5. Put attitude into it (but be genuine)
To entertain people you need to demonstrate emotion in your voice, whether that's heartbreak or a cocky confidence. You can use all sorts of stylistic tricks to keep things interesting and express your musical ideas, but don't overdo it. Sometimes simplicity is best.
Also, I think it's nice when pop singers use their actual accents instead of merging into some form of faux-American accent. Missy Higgins makes her strong Australian accent charming (quite a thing for a Kiwi to admit!) and I love Paolo Nutini singing in a Scottish accent.
6. Communicate the words
If you've gone to the trouble to write lyrics (or choose a song with lyrics you like) then make sure the words are clear. Put tiny spaces between each word. Spit out your consonants (more than you think you need to) and be clear about differences for example between 'd' and 't'. Try saying 'The tip of the tongue, the teeth and the lips' with exaggerated mouth movements to limber up.
So if all this has inspired you, something you could think about is joining a local all-comers choir. If you're a beginner, look for one with no audition and no requirement to read music. There are plenty of choirs like Bristol's Riff Raff Choir who sing a range of stuff including pop and rock.