Well, Vector already gave pretty good tips, so I will just give some of my thoughts about mixing and how I mix.
The first thing you should paying attention when talking about vocals is compression. You need a lot of compression and probably you will need to have more than one compression on, and when you think it's enough add more compression! XD Okay, I'm kidding, but compression really brings out more warm, more foward, to your vocals and make them sound less muddy. Don't forget that compression's function is to equilibrate the volume of your whole sample by making everything sound more or less in the same volume, so it's not necessarily a tool to change your vocal's tone, but it really helps to bring out more warm to your vocals.
Try messing around with as many compressors you want in your vocal chain and you will see how much is enough to you. For you to have an idea I use 3 compressor, a equalizer and a saturator. Maybe I'm using too much? Maybe, but I think it's pretty great so far so why not? I wanted to give an example, but almost all sound host sites seems to add their own effects to the audio samples in their own way. So how I hear the original sample will not be the same way you hear it.
For eq is pretty cool for you to understand the "vocal zones" and how each one of them will affect the audio if you boost or cut them.
- 20 to 300 Hz: body and muddiness.
By cutting or boostin these frequencies you will change the lower frequencies of a singers voice what can give them more presence through the whole sound spectrum or make their voice thinner. Usually I would recommend you go at least to 120 Hz, cutting more than that is crazy (Also, we usually cut this part since it can also have some microphone audio interferences).
I like to cut this part in 68 Hz, it gives me enough low end and don't make the voice too thin, but it's different to every vocal so you will probably need to test it yourself.
Do you know when a singer sings too much "inside"? Like if their voice is inside their throat and not projecting out of their mouth? That's more or less what we mean by boxiness. When a singer's voice seems to be inside a box and not resounding properly you will want to cut this frequency area to make it sound more harsh.
Good examples of Vocaloid boxed vocals, in my opinion, are Luka and Merli. They are soft, but not like Aoki Lapis that is airy, more like if they are shy singing and are singing quietly to themselves.
Well, as a CUL user I know this one a little bit XD Do you know when your vocals sound too nasal? Like if the voice is resonanting in their nasal cavity and making it sound kinda annoying? If you don't have idea of what nasality is hear this video and pay atenttion to CUL's "i's":
CUL has very strong "i" samples (and very nasal too) so she is a pretty good example of nasality. By cutting out the nasal frequency area you can make her "i" not so highlighted and give her a more stable vocal tone.
I don't understand too much about this one, but if I'm not wrong it will bring out your vocals more to the front of your mixing if boosted, and if cutted will do the opposite. You should consider to boost it when the instrumentals are way higher than your vocals.
- 4 to 7 kHz: sibilance.
- 10 to 15 kHz: air.
I don't know too much about sibilance and I really thought that sibilance and air were the same area XD So I will just say about how I use it. I like to boost at 6 kHz to make the vocals a little more harsh and audible through the mix. If the vocals are too airy I don't boost it and sometimes I even cut a little, but it really depends.
Also, don't forget to download Free plugins since, unless you're with a good (usually not free) DAW, some of the necessary plugins to vocal mixing aren't too good/easy to use for mixing as free options. Here is a list of plugins types I think you should look over:
-> Compressor;
-> Equalizer (Parametric equalizers are pretty good for newbies like us! o/);
-> Saturator;
I also like to hear the instrumental to see where I need to put my vocals. If you hear the original instrumental you will perceive that usually it lacks something. It's almos like there is a place inside the song that was created to insert the vocal, but since it's just the instrumental there is no voice out there. So I recommend you to pay attention to it and see where your vocals need to be placed, like, is it near to the guitars? Or the piano? And yada, yada, yada (Usually I like to think it's near string instruments, snares or wind instruments (like flute and recorders)).
For more professional mixing you need to consider a lot more, like multi tracking and adding certain effects to your voice in certain moments. There is also a process called automation that controls your vocals dynamics through the song and can be used to make your vocals more complexes, but since I know nothing bout it (Because I'm not a professional mixer yet XD) I will not talk anything about it, just mentioning it here for you to understand that vocal mixing is a little more complex than just the vocal proccessing tips I gave you (You probably already knew about it).
That's it, hope I helped you! ^3^/ Remember, this is just how I do my mixing and every voice is unique, so what works for me will probably not work completely for you. Don't be a perfectionist tho, if something sounds good to you so it's okay, no need to worry that much since your mixing skills will growl naturally over time.
And don't forget: never stop learning and enjoy the proccess! In the end we're all doing it to have fun, aren't we? ^3^/
Goodluck and byebye!