[This post turned into rather a marathon - it's a lot of text, but i hope it's helpful and/or reassuring - let me know if it doesn't cover a topic you need!]
So, you fell in love with a vintage pattern, it wasn't all that expensive... add to cart, wait for package... now it's in your hot little hands, and you're starting to think, "er, now what?"
Well, here's my set of suggestions (this assumes you're sewing for yourself, and are reasonably comfortable following a current pattern, but are tackling a vintage pattern for the first time):
Trace your pattern. Always, always trace your pattern. The conservator in me begs you, do not alter your original pattern, do not tape it to anything or - God forbid - iron it onto a fusible interfacing to support it (i've seen people suggest this, really, and it made me weep). Just trace it. If you've traced your pattern and something goes wrong in fitting or grading, you can chuck your altered tracing and go back to the original. If you're fitting on the original, there's no "undo" for whatever you've done. It will save wear on your vintage pattern, it will save wear on your nerves.
I like to use the pattern tracing stuff they sell. You'll find it with the interfacings at the fabric store - there are a couple of brands - Tru-Grid is one brand, Red Dot Tracer is another - but they usually have some sort of dot or grid (at a 1" interval, at least on this side of the pond), and they're just see-through enough that it's pretty easy to transfer all the markings from the original pattern piece. If you want to save the expense (or start right-now-this-minute), paper - kraft, freezer paper, tissue, etc. - will get the job done.
Grade, if you need to (if you've been lucky enough to find a pattern in your size, you can skip this, and go on to the next step, fitting). Grading is the process of making a pattern larger or smaller to fit a different size human. There are different ways to go about it, so find a method that makes sense to you, and gives you good results. There are descriptions i've found useful here and here, and with grading, as elsewhere in the process, a good sewing or costuming book may be a help to you. If you've sewn from a modern multi-size pattern, you'll have some idea of how the different sizes relate to each other, but sometimes it helps to think about it in three dimensions, not just flat (makes it easier for me, anyway, but flat drafting isn't my strong suit...).
Make a muslin. Do this for the same reason you trace the pattern, except that what it saves is fabric and swearing. The fit of vintage clothing is different, and garments may have more or less ease than you're used to. The patterns will be designed to fit over the appropriate/fashionable undergarments of the day; if you don't have - or don't wish to deal with - said undergarments, know that (a) you may need to adjust the fit to account for that, and (b) it will change the look of the finished garment.
Making a muslin doesn't necessarily mean it's made out of muslin - best to choose a fabric with similar weight and drape to what you plan to use for the actual garment. Vintage patterns may or may not give fabric suggestions. Fabric suggestions may or may not prove helpful - they may suggest fabrics that can't be had readily now, for instance. So you need to have some idea what sort of fabric will work for the design you're looking at. This is knowledge gained only by experience - sadly, often the experience of having picked the wrong sort of thing and being underwhelmed with a finished garment. But forewarned is forearmed, so if you're not sure what will suit, look at vintage garments with a similar design for guidance. (In some cases, you can also cheat by underlining, but that's a post for another day...)
Start by pin-fitting your traced pattern - pin the seams, darts, and so forth, and try it on (carefully!), to see where you may need to adjust. Make your basic adjustments for fit - pin or tape on extra tissue or tracing material where you need it, mark anywhere that needs to have less fullness - and use the altered tracing to cut your muslin. Pin or baste the muslin together (i tend to baste, because it's less, um, pointy in fitting - and also less likely to come loose at an inopportune moment).
Once the fit of your muslin makes you happy, take it apart where you have basted it, and use it as a pattern to cut your actual fabric. When you reach this point, you'll probably find that the process of following a sewing pattern hasn't changed much. The instructions and construction methods are generally pretty similar. You will, from time to time, find something vague and inscrutable in the instructions, but in my experience, that's no different from current patterns, either. One caveat: if your pattern is earlier than, say, the 1930s, directions may be scanty or even entirely lacking - be aware of that if you want to tackle something that early.... Again, having that sewing book nearby will be handy (i find many vintage ones excellent, and if you've got one from the same time as your pattern, even better) to get you through any vague bits. A sewing book that's vintage may also help clear up any difficulties in "translation" of terminology that's changed over time (e.g. "slide fastener" = zipper). I recommend making notes of all your changes as you go, either on your altered pattern pieces or on a piece of paper you can tuck into the pattern envelope, so you've got a record of what worked if you want to use that pattern again later.
There are a lot of steps, it's true. But the good news is that none of them are extremely difficult, and none of them are matters of life and death. By tracing your pattern and making a muslin, you get insurance against fitting issues and the inevitable sewing "oops" - you can always start over (and hey, the mistakes are tremendously educational, so it's not even like you wasted that time...).