What are the basic calculations you're referring to? Other than doubling/having shutter speed or ISO when I open/close the aperture a stop I don't find myself doing any, I just fiddle with the settings 'till the image looks right on the LCD. After a while you get a feel for what settings work in what circumstances and the process becomes much quicker.
Here's an example of where I bluffed my way through an entire shoot in manual mode with manual flash, just using the camera's LCD screen as a guide:
This headshot of Oliver, editor of law journal Ebor Lex, done in a standard meeting room in a very short timescale. I thought it would be an interesting subject for a "stream of consciousness" post showing every shot that was taken during set-up and and trying to explain what was going through my head at the time. This is not supposed to be a perfect example of how it should be done, merely a record of how it was done.
It's important to have some idea what you're trying to achieve before you start so I decided I wanted something edgy, like this shot but with a more traditional background. That look was achieved by having a pair of softboxes very close to the subject, angled slightly toward the camera so I started off with the lights in that position.
No light meters no modelling lamps, what follows is exactly what I saw on the back of the camera at each stage...
I didn't have a wide lens with me so no setup shot but here's a diagram to help you visualise what's going on.
First step, set up the background light (a projector screen makes the perfect background). I used a bare speedlight angled down so that the natural falloff would provide a nice gradient from light to dark. It's close to the screen with no light modifiers so it will be nice and bright so I set it on something like 1/4 power on for faster recharge. The camera is in manual, max shutter speed I can use with flash is 1/200s, for safety I go one setting lower, 1/160s. Middle of the road aperture of f/5.6, two stops down from wide open. ISO 100. Subject in place. Bang.
The image as it comes up first is on the left, I hit the "info" button straight away to get the histogram view (right). Background is a bit darker than I wanted, so I crank the flash up a stop. Bang.
That's better. The blinking area on the info screen indicates pixels which are blown out (i.e. have hit 100% white) since the camera can't record more than 100% white detail is likely to be lost. As the background is plain and I want it to be white I'm not bothered by this. I turn the background light off and the main light on. It's in close so power is set low. Bang.
Notice the timestamp (14:46), one minute has elapsed so far! The light is more extreme than I wanted. Move the softbox toward me a little. Talk to the model, explain what's going on. Bang.
Light is still too oblique. Move it round a lot, which involves moving the table slightly and costs some time. Bang.
Getting there, but need to move the light a little bit more to throw some light on the other side of Ollie's face. Decide to move the tables out of the way completely, which takes a few minutes (pro-tip: move the furniture before you begin, or better still, get someone else to do it for you). Bang.
That looks like what I want but it's overexposed. Instead of moving I drop the ISO a stop to 50 (there's very little difference between ISO 50 and 100, we're not taxing the DR or noise here). Bang.
Little is still a little to bright (see blinkning image, right). Can't lower the ISO so I have to power the flash down a little. Bang.
Main light is how I want it, now I position the fill light. I've deviated from the original symmetrical setup in favour of a strong light from the left so I move the smaller softbox back to provide a glancing rim light. Use the same setting as the main light, knowing it'll be darker as it's further away. Bang.
Looks pretty good, there is still a little bit too much shadow on the face so I move the fill light closer in and toward me. Reassure model that we're almost there. Bang.
Both lights are how I want them, The image is a little overexposed but nothing RAW can't cope with. The purpose of turning off the back light was check the main lights don't interefere with it. As you can see they clearly do, but they add a uniform pattern of light so all I have to do is turn the background light down a stop to compensate. Bang.
All looks fine, take a step back (I'm using a prime lens) to give wider view for more cropping options. Accidentally nudge the shutter speed to 1/100s (the flash is easily overpowering the flourescent room lights so it's not a problem). Explain to the model we're going for a take. Bang.
Zoom in and check the pose, all looks good. Explain to the relieved model he can relax now. Time from the first test shot to completion: 11 min. Pack up, go home. Here is the final lighting set up:
I filled in the shadows a little in the raw conversion, applied a few curves adjustment layers in photoshop and tweaked the colour balance. Finally the image was rotated slightly and cropped, leading to the finished version (click for larger):
Sure there are charts of aperture vs shutter speed vs ISO in different types of light, but you then have to judge the light, just as there are charts of hyperfocal distance vs subject distance etc. but you have to judge your subject distance, so instead of doing that and then looking up an f-stop value, why not just learn to judge what aperture you need straight off and not have to rely on a data sheet?
Digital is very good for trial and error shooting so my advice is to just get out there and wing it, since cheat sheets are only as good as your judgement anyway.