The same way you round any decimal fraction to the nearest tenth. Look at the digit in the hundredths column. If it is 5 or larger, increase the digit in the tenths column by 1, otherwise leave the digit in the tenths column alone. Only report your answer with one decimal place of accuracy.
Also note that if your square root is the root of a perfect square and the answer is a whole number, you have to add the .0 on the end to make it rounded to the nearest tenth.
For example:
Rounded to the nearest tenth, 1.4
Rounded to the nearest tenth, 9.7 (the hundreths digit is > 5, so plus up the tenths)
But rounded to the nearest tenth, 10.0
John
My calculator said it, I believe it, that settles it