In this formula:
=INDEX(Sheet1!B:B,MATCH(A1,Sheet1!A:A,FALSE))
MATCH returns the number of the row containing the value in A1. That row number is passed to the INDEX function which returns the value in column B.
If this data is in A1:E5 on Sheet1:
<TABLE style="WIDTH: 216pt; BORDER-COLLAPSE: collapse" cellSpacing=0 cellPadding=0 width=288 border=0 x:str><COLGROUP><COL style="WIDTH: 36pt; mso-width-source: userset; mso-width-alt: 1755" width=48><COL style="WIDTH: 31pt; mso-width-source: userset; mso-width-alt: 1499" width=41><COL style="WIDTH: 42pt; mso-width-source: userset; mso-width-alt: 2048" width=56><COL style="WIDTH: 44pt; mso-width-source: userset; mso-width-alt: 2157" width=59><COL style="WIDTH: 63pt; mso-width-source: userset; mso-width-alt: 3072" width=84><TBODY><TR style="HEIGHT: 12.75pt" height=17><TD class=xl22 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; WIDTH: 36pt; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" width=48 height=17>Vessel</TD><TD class=xl22 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext 0.5pt solid; BORDER-LEFT: windowtext; WIDTH: 31pt; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent" width=41>Type</TD><TD class=xl22 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext 0.5pt solid; BORDER-LEFT: windowtext; WIDTH: 42pt; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent" width=56>IMO</TD><TD class=xl22 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext 0.5pt solid; BORDER-LEFT: windowtext; WIDTH: 44pt; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent" width=59>Call Sign</TD><TD class=xl22 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext 0.5pt solid; BORDER-LEFT: windowtext; WIDTH: 63pt; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent" width=84>Flag</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl22 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>SHIP 1</TD><TD class=xl22 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent">AHTS</TD><TD class=xl22 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent" align=right x:num>9487201</TD><TD class=xl22 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent">9VLG5</TD><TD class=xl22 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent">SINGAPORE</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl22 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>SHIP 2</TD><TD class=xl22 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent">AHTS</TD><TD class=xl22 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent" align=right x:num>9544669</TD><TD class=xl22 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent">9V8231</TD><TD class=xl22 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent">SINGAPORE</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl22 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>SHIP 3</TD><TD class=xl22 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent">PSV</TD><TD class=xl22 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent" align=right x:num>9482469</TD><TD class=xl22 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent">9VHM5</TD><TD class=xl22 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent">SINGAPORE</TD></TR><TR style="HEIGHT: 12.75pt" height=17><TD class=xl22 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext 0.5pt solid; BORDER-BOTTOM: windowtext 0.5pt solid; HEIGHT: 12.75pt; BACKGROUND-COLOR: transparent" height=17>SHIP 4</TD><TD class=xl22 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent">PSV</TD><TD class=xl22 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent" align=right x:num>9482457</TD><TD class=xl22 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent">C6XD4</TD><TD class=xl22 style="BORDER-RIGHT: windowtext 0.5pt solid; BORDER-TOP: windowtext; BORDER-LEFT: windowtext; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent">BAHAMAS</TD></TR></TBODY></TABLE>
and B1 on your active sheet contains SHIP 1, the following formulas will return IMO, CALL SIGN and FLAG:
=INDEX(Sheet1!C:C,MATCH(B1,Sheet1!A:A,FALSE))
=INDEX(Sheet1!D:D,MATCH(B1,Sheet1!A:A,FALSE))
=INDEX(Sheet1!E:E,MATCH(B1,Sheet1!A:A,FALSE))