There are lots of really good YouTube tutorial videos on this topic, search on "how to make a lead vocal stand out in a mix."
 
The basic concept I had to grasp was that before I could push the level of the lead vocal up I needed to make the lead vocal track "ear friendly" by applying subtractive EQ and compression to it. I think of it as getting ready to pet a kitten. I'm softening the touch. Which is not to say I'm making it wimpy, it works for any sound, light pop, metal, whatever.
 
With a parametric or linear EQ (the one in ProChannel is excellent for this), I find the one or two worst "honk" frequencies (again, search for how to find and cut honk frequencies out of an audio track), and cut them by about 3dB. I also roll the very low stuff off with a high-pass filter, up to at least 150Hz. Then I apply a clean compressor at 4:1 ratio until it's taking about 4-5dB average off, if it's a pop song.
 
Season to taste, this is where I start. Once you get that going, you may find that you can take that vocal track and bring it up without it sounding like it's walking all over everything else. It can be louder without dominating, and it can also be softer while still being intelligible. The listeners' ears will feel "safe" listening closely to elements that have been processed this way because they will not be jabby.
 
I throw the same recipe on acoustic instruments as well with good result.
 
A CA-2A or similar "soft, slow" compressor after all that, on the track or on the vocal bus if you have backing vocals or doubled or tripled vocals will further smooth and shine and also help "glue" whatever's in the bus together for you. Search for "stacking compressors."

All good suggestions above, but many of the suggested steps, e.g. applying compression, are for later in the process. You have to start with some coarse leveling and normalization to get in the ballpark, and only then proceed to EQ and compression.
 
When you are your own engineer, it's difficult to monitor mic levels to keep them within a safe-but-hot range, so we all tend to err on the side of caution and be conservative when tracking. This often results in levels that are too low and/or inconsistent. But even the wildest swings in level can still be molded into a steady up-front vocal track.
 
First step is coarse normalization. Play back the vocal track and note its highest peak value. This is to determine how much headroom you're starting with, and to identify which clip is hottest. If it's -12 dB or higher, no normalization is required and compression alone can handle the volume boost. If not, use Process -> Gain to boost it accordingly. You can apply a surprising amount of gain without harming the take. I've boosted vocals by 40 dB without significant noise issues (although those were cleanly recorded in a very quiet room).
 
Next, apply gain to each of the quieter clips so they get closer to the hottest one identified in step one. The easiest way to do this is via a gain plugin that can be automated. I use Blue Cat's gain plugin - it's free, fully-automatable, with adjustable range and the ability to link multiple instances to one automation lane. It's important to do this before applying any effects. If there are any notable "woofs" or sibilance in the performance, you can also use gain automation at this time to mitigate them.
 
It's only after you've achieved consistent volume across the entire track that it's time to apply remedial EQ (as opposed to creative tone-shaping EQ). Talking mainly about high-pass filtering. You want to remove any excess low-frequency energy before the signal hits the compressor. 
 
I'll let others rattle off their favorite compressors and compression techniques. All of the above should happen before you even think about which compressor to stick in. 
 

Craig Anderton, thank you for all your amazing contributions!

Wow, some great suggestions. Thanks for the time. I'll have to  spend some hours with trying to understand it all.
However I'll start with one of the  earlier suggestions: 1)duck the music with the vox using a side chain.
2)Also push the music out to the sides to clear out the middle. leaving the drums and bass there. And put the vox in the center.
I definitely understand the 2nd item; that is, about panning. Re: duck the music with the vox using a side chain.
I  have no idea what "duck" or "vox" means. I also wouldn't know a side chain if it hit me in the knees (from the side, naturally.) I guess I'll have to look that up. I actually really have heard of  side chains, but just wouldn't  know where to find them.
I like the idea of looking at some videos as well, though, as I said, I'll also try to go thru each recommendation 1 by 1.
Thanks again.
LNovik

Try this site below and then tap videos.
 
https://www.youtube.com/user/recordingrevolution/videos?disable1

Hi LENovik.
 
I know it all gets confusing at first, no problem.  "Duck" in this context means lowering the volume of something(s) for a period of time.  "Vox" is just shorthand for "Voice" or "Vocals".  As for "Side-Chain", here is a straightforward article that explains the use of a compressor's side-chain input and how to use it for "ducking" your music volume under the volume of your "vox" track(s)> --> http://www.practical-music-production.com/sidechain.html
 
Good luck, -DAve

Too much of the advice being given is putting the cart before the horse.

Step ONE happens in preproduction: arrange the parts so that there is a hole in the frequency spectrum for the vocals to sit in. If you have a bunch of instruments and a vocal fighting for the same space in the mix, you are starting out behind the power curve and the vocals will probably loose.

Step TWO: the vocals are the most important thing in the mix. Everything else exists to support them. Adjust the levels of the other instruments to fit them, not the other way around.

Step three is to use complimentary eq to - you guessed it - carve out a hole in the frequency spectrum for the vocals to sit in. If you emphasize a particular frequency on your vocal, cut it on everything else.

If you do all the stuff I mentioned, then your mix is gonna be probably about 90% done before touching any faders, compressors or anything else for that matter.

bdickens
Too much of the advice being given is putting the cart before the horse.

Step ONE happens in preproduction: arrange the parts so that there is a hole in the frequency spectrum for the vocals to sit in. If you have a bunch of instruments and a vocal fighting for the same space in the mix, you are starting out behind the power curve and the vocals will probably loose.

Step TWO: the vocals are the most important thing in the mix. Everything else exists to support them. Adjust the levels of the other instruments to fit them, not the other way around.

Step three is to use complimentary eq to - you guessed it - carve out a hole in the frequency spectrum for the vocals to sit in. If you emphasize a particular frequency on your vocal, cut it on everything else.

If you do all the stuff I mentioned, then your mix is gonna be probably about 90% done before touching any faders, compressors or anything else for that matter.

This is really good advice, especially item #1.  You gotta start with a good arrangement.  Listen to some songs in the same style you're trying to record and you'll get an idea of what to do.  One of the things that surprised me when I really started listening to arrangements is how little is going on while the singer is singing.  Usually it's only bass, drums, some type of bed (maybe one guitar or keyboard) and the singer. 
 
Good luck.  And if you get stuck come back here and post your song.

Thanks for that last reply, Jude77. Of course, I've heard of keeping frequencies separate, so as to make room for each spectrum. It just seems so NON-intuitive to me. I guess I could see it if I were singing "Jingle Bells," which only goes from C to G. But most songs are sung over at least an octave, I would think. The bass guitar and bass drum would be easy  with this, but what about piano and guitar--and other percussion sounds? I think of posing in a picture with several other people; if I wanted to be noticed, or stand out, it seems I would have to distort everyone else to be either much shorter or taller, so that each one of them would have their bodies compressed into about 12 inches starting above my head, or below my knees! I would look cool, but they would look like pygmies! 'Not that there's anything  wrong' with pygmies!
Yes, I do realize that I'm missing something, and EQ'ing is something I'll eventually have to learn, so  what I'm asking is: is their a  program where I can add each track to it and it (the program) assigns frequencies to each part? So I could see what's being done in real time.
And I  DO really appreciate the fact that you said I could upload the song on this site eventually, and some people might have the time to make suggestions. Not quite ready for that, since I have a demanding and time consuming daytime job.
Thanks again.
LNovik

And now, as I reread these helpful notes, I see this by dubdiscipline. 
 
Use a good analyses like the free SPAN meter by Voxengo to see if your instrumental is fighting your vocals for space. 
 
So, I'll look up this item. 
 
LNovik