@Shadow Wizard's answer is correct as per the TV-Show.
I'd like to add the books' description of the blades which may help to identify how people can instantly recognise the Valyrian Steel blades.
This is Bran's description of Ice (the ancestral sword of House Stark):
“Ice,” that sword was called. It was as wide across as a man’s hand, and taller even than Robb. The blade was Valyrian steel, spell-forged and dark as smoke. Nothing held an edge like Valyrian steel.
-A Song of Ice and Fire: Book One - A Game Of Thrones, Chapter One (Bran I).
And This is Jon's description of Longclaw:
When Jon turned it sideways, he could see the ripples in the dark steel where the metal had been folded back on itself again and again. “This is Valyrian steel, my lord,” he said wonderingly.
-A Song of Ice and Fire: Book One - A Game Of Thrones, Chapter Sixty (Jon VIII).
You see what I'm getting at here: Valyrian Steel blades have a distinctive 'ripple' effect from the folding technique used to forge them. They are also quite 'dark' and 'smoky' in colour. This is very distinctive and instantly recognisable.
The blades used in the TV-show are not 'dark' or 'smoky', but people can still recognise the blades instantly by their distinctive 'ripple' effects and immaculate sharpness.