A dictionary of Confusable Phrases: More Than 10,000 Idioms and Collocations

Note:
The expression does not correlate in meaning with the
phrase give someone leg—(sl.) deceive or fool a person: Last time
I saw you, you’re giving me a little leg about there’s nothing
going on.
give someone a glad hand • give someone a good
hand
give someone a glad hand —(also: glad-hand someone) give a
person a cordial handshake or greeting: Crude economic rea-
sons do not explain why he should have been given the glad
hand.
give someone a good hand —(also: give someone a big hand)
give a person a large round of applause: The club enjoyed her
talk and gave her a good hand at the end.
give someone a hand • give someone one’s hand
give someone a hand —
1
. help smb. with a task, etc.: Give
me a hand with this case, will you? 2. applaud a person: Come
on, give them a hand. They did very well.
Note: 
The expression does not correlate in meaning with the
phrase give someone a free hand—give smb. freedom of action
in affairs: He accepted the job after the prime minister agreed
to give him a free hand in key economic issues.
give someone one’s hand —
1
. agree formally to smth.: Yes, I
agree to your marrying my daughter, and I give you my hand
upon it. 2. (of a woman) agree to marry a man: Bruno and
Evandra have loved each other for six years, but she refuses to
give him her hand.
give someone a head • give someone his head
give someone a head —(of alcohol) cause headache: He goes
on to tell us that, “It won’t give you a head in the morn-
ing.” He speaks with the authority of a man that knows his
drink.
give someone his head —
1
. (of a horse) not to check or hold
in with the bridle: He has always been a well-mannered colt,
but I have never been able to give him his head. 2. give a per-
son freedom to have his way: He’s got some great ideas. Why
not give him his head and see what kind of campaign he comes
up with.