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Nobody likes a vacancy as it means nobody's making money.  Keeping a vacancy as short as possible is one of the most valuable jobs a property manager can do for an owner.
Owners first need to budget for vacancies and expect them.  It's unrealistic to think 100% of your units will be 100% occupied.  Even if you have responsible reliable long term tenants life happens and people will occasionally move.
So how can you get those properties filled as quickly as possible?  First get them ready to show.  Here's where it pays to know your market.  If you're new at landlording surf the net and check out your competition on craigslist or other websites.  If your competition is holding open houses show up at one and take note of upgrades and amenities.  What are the salient points stressed in your competitors' ads?  That will help you decide what improvements will draw applicants.  In my area of Southern California garage space isn't a deal breaker but if you're in a colder climate it may be.  Some areas that I cover prefer hardwood floors to carpet.  Other areas find every landlord willing to accept dogs.  Do your homework and know your local market and then improve your units accordingly.
The cheapest improvement is fresh paint.  Pick neutral colors but be more adventurous than the ubiquitous Swiss Coffee.  If the kitchen has wooden cabinets instead of painting top and bottom cabinets white make the bottom ones slightly darker.  No price difference for you and your units will stand out.  If your budget for improvements needs improvement at the very least make the unit sparkling clean and paint if at all possible.
Okay, the work's been done, ready to show, now what?  Back to researching your market.  Price your unit competitively.  If you want to try for a higher price don't hang onto it for too long.  If you don't get any bites after 2 weeks, time to lower.
Put up signs, load the listing on your website, place internet ads and respond quickly to calls or emails. 
During slower markets or times of year you may want to offer an incentive.  In a multi unit building you may offer a rent credit to exisiting tenants for anyone they refer who signs a lease.  You may advertise 13th month free to qualified applicants. 
If your unit shows well and you've had several viewings but no applications your price is probably too high.
In your haste to rent don't skimp on your screening.  Remember the only thing worse than a vacant unit is an occupied unit and a tenant who isn't paying.  Or even worse than that an occupied unit with a tenant who isn't paying and is damaging your property.