Women's Rights
Let's deal with the biological facts first. Compared to the typical male, women have longer leg bones and shorter upper body dimensions. They also weigh less and aren't as tall as a bloke. Their pelvis bones are wider to allow for sprogging, putting the 'sit bones' which comfortably support body weight on the saddle further apart too. All this genetic make-up significantly affects what constitutes an ideal woman's bike. The frame will generally be smaller but, most importantly, it should be shorter so it can be easily reached. Several companies are producing frames with altered proportions and a woman's tag, but the recent rash of 'jumping/dual' bikes are generally built shorter for more maneuverability as well.

Scott Contessa 20
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As rider weight is lower, suspension settings -- both spring weight and damping - need to be lighter as well to achieve the same performance level. Rear shock spring weights on Marins, Scotts, Treks, Specializeds and others are already altered to suit the size, and air pressure is of course totally adjustable (but needs damping to match), but it seems to be a different story up front.
Unfortunately, manufacturers want bulk discount on their fork orders and if they start asking for different internals for a small number they'll have to fork out more. But several fork manufacturers make softer spring versions, Manitou market their Diva range as women specific forks, and we see them cropping up on many women's bikes now. Air forks allow custom set-ups and are lightweight too, ideal for lightweight and women riders.
Get a grip
Hand size is also crucial as many brakes will be out of reach in stock set-up. Most levers can be reduced in reach, but this often means less cable pull, clearance and power, and specific short-reach levers are hard to find. Large grip diameter can also cause aching and fatigue in small hands -- this also applies to bar-ends. Wide bars will also stretch arms and shoulders but a few minutes with a hacksaw should provide lasting relief. Women's saddles are widely available with broader profile and centre cut-outs to reduce pressure on sensitive areas, but preferences vary on shape and padding levels, so try as many as possible before parting with your dosh.

Trek Fuel EX9 WSD
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Many of our female testers also find rear shocks or a suspension seatpost a welcome addition. On the componentry front, the basic consideration is that women are less powerful than men in terms of potential wattage output, and lighter in their riding style and physical make-up. This means low bike weight is more of a concern than durability. Light bars and seatposts, featherweight rims, radial spoking and lighter tyres are all a bonus to female riders.
Unfortunately, lighter components nearly always cost more, and current women's bikes generally sit in the budget to mid range of the market, so you're generally looking at aftermarket upgrading to really lose weight.
If your partner or friends insist on inflicting their cast-offs on to you, then at least make the following checks to insure you continue to enjoy your riding.
Frame: It has to be within spitting distance of the right size. At least a couple of inches of crotch clearance over the top tube and enough seatpost still inside the frame.
Suspension: Whatever you've got it needs to be readjusted to suit new rider weight. If you're light and you can't find the appropriate soft spring set, just try removing the spring stack on one side. Lots of forks only have the spring on one side anyway and it'll certainly feel plusher.
Componentry: It's that old chestnut about beginners needing equipment that functions flawlessly as they've enough other stuff to fret about. And remember that women will benefit from lighter components and especially wheels. So don't accept any worn out or heavy components that have been dragged out of the cupboards or shed.
Saddle: If it's really not comfy then don't try to get used to it, you'll just end up making excuses to not ride and it'll all end in tears. Buy quality and think of it as investment.
Stem: Yes, they alter reach but they also radically affect handling. A shorter stem may stop a big bike feeling like a torturer's rack, but it'll be almost impossible to keep in a straight line -- which tends to unnerve novices. On the flipside, a long stem makes a bike feel bigger but it'll develop an extremely stubborn attitude to changing direction.
Tyres: They're either bald or were got rid of for a reason. Often OEM tyres are cheap and heavy, and replaced after only a few rides. So test ride them by all means but change them if you're not happy with grip or cornering, a good tyre can make all the difference to confident riding.