The ideal way to send blessings upon the Prophet (blessings and peace of Allah be upon him

Sending blessings upon the Prophet (blessings and peace of Allah be upon
him) is one of the greatest acts of worship encouraged in Islam, and it is
one of the most beneficial supplications for a person in this world and the
hereafter, and it is one of the requirements of loving, venerating and
respecting the Prophet (blessings and peace of Allah be upon him) and giving
him his rights. 

With regard to the ideal way of sending blessings upon the master of mankind
(blessings and peace of Allah be upon him), there are a number of ways of
doing that, which you can find in the book Sifat Salaat an-Nabi (sall-Allahu
‘alayhi wa sallam) by al-‘Allaamah al-Albaani (may Allah have mercy on
him), p. 165 of the edition published by Maktabat al-Ma ‘aarif in Riyaadh
[this book is available in English as The Prophet’s Prayer Described].
Among the soundest and most well-known of these ways are the two ways that
the Prophet (blessings and peace of Allah be upon him) taught his Companions
(may Allah be pleased with them) when they asked him how they should send
blessings upon him (blessings and peace of Allah be upon him). These two
ways are as follows: 

~1~

“Allaahumma salli ‘ala Muhammad wa ‘ala aali Muhammad kama salayta ‘ala
Ibraaheem wa ‘ala aali Ibraaheem, innaka hameedun majeed. Allaahumma baarik
‘ala Muhammad wa ‘ala aali Muhammad kama baarakta ‘ala Ibraaheem wa ‘ala
aali Ibraaheem, innaka hameedun majeed (O Allaah, send prayers upon
Muhammad and upon the family of Muhammad, as You sent prayers upon Ibraaheem
and upon the family of Ibraaheem; You are indeed Worthy of Praise, Full of
Glory. O Allaah, send blessings upon Muhammad and upon the family of
Muhammad as You sent blessings upon Ibraaheem and upon the family of
Ibraaheem; You are indeed Worthy of Praise, Full of Glory).”

Narrated by al-Bukhaari (3700) and Muslim (406) from the hadeeth of Ka‘b ibn
‘Ajrah (may Allah be pleased with him). 

~2~

“Allaahumma salli ‘ala Muhammadin wa ‘ala azwaajihi wa dhurriyyatihi kama
salayta ‘ala Ibraaheem, wa baarik ‘ala Muhammadin wa ‘ala azwaajihi wa
dhurriyyatihi kama baarakta ‘ala aali Ibraaheem, innaka hameedun majeed
(O Allaah, send Your salaah (grace, honour and mercy) upon Muhammad
and upon his wives and offspring, as You sent Your salaah upon
Ibraaheem, and send Your blessings upon Muhammad and upon his wives and
offspring, as You sent Your blessings upon the family of Ibraaheem. You are
indeed Praiseworthy, Most Glorious).” 

Narrated by al-Bukhaari (3369) and Muslim (407) from the hadeeth of Abu
Humayd as-Saa‘idi (may Allah be pleased with him). 

The Prophet (blessings and peace of Allah be upon him) did not choose
anything but that which is noblest and best. 

See: Rawdat at-Taalibeen by an-Nawawi (11/66); Fath al-Baari
by Ibn Hajar (11/166); Sifat Salaat an-Nabi (sall-Allahu ‘alayhi wa
sallam) by al-Albaani, p. 175; al-Mawsoo‘ah al-Fiqhiyyah al-Kuwaitiyyah,
27/97 

It is better to vary the phrases used, switching between the versions that
have been narrated, sometimes reciting one and sometimes reciting another,
so as to follow the Sunnah and sharee‘ah, and so that always reciting one
version does not lead to neglecting another which is also proven, and
because there are many other benefits in doing so which will not be attained
by always reciting only one and not the other. 

But we should point out that it is not prescribed to combine and mix these
phrases so as to produce a combination of all of them in one; rather that is
contrary to the Sunnah, as was stated by a number of scholars.

See: Majmoo‘ al-Fataawa by Ibn Taymiyyah (22/335, 458; 24/242, 247);
Jala’ al-Ifhaam by Ibn al-Qayyim (p. 373 ); Qawaa‘id Ibn Rajab
(p. 14); ash-Sharh al-Mumti‘ by Ibn ‘Uthaymeen (2/56, 65; 3/29, 98). 

All of this has to do with sending blessings upon him (blessings and peace
of Allah be upon him) after the Tashahhud in the prayer. 

With regard to sending blessings upon him (blessings and peace of Allah be
upon him)) by saying “Allahumma salli ‘ala Muhammadin wa aali Muhammad
(O Allah, send blessings upon Muhammad and the family of Muhammad) outside
of the prayer, if what your friend means is that it is lacking in comparison
to the complete wording that has been narrated, then this is correct. But if
what he meant was that it is not valid or that it does not count as sending
blessings upon the Messenger (blessings and peace of Allah be upon him),
then that is not the case; rather it is sending blessings upon the Prophet
(blessings and peace of Allah be upon him) and its wording is correct and
fulfills the purpose. The scholars still say, “Allahumma salli ‘ala
Muhammad” or “sall-Allahu ‘alayhi wa sallam (may Allah send
blessings and peace upon him)” and the like. The matter is broad in scope,
in sha Allah. 

Al-Haafiz ibn Hajar stated in Fath al-Baari (11/166) that the
majority of scholars think that any wording that fulfills the purpose of
sending blessings upon him is acceptable, but in the prayer one should keep
to the wording that has been narrated and not omit any part of it, so as to
be sure of following the Sunnah and what is narrated from the Prophet
(blessings and peace of Allah be upon him). 

With regard to this wording also, it is restricted to sending blessings (salaah)
and not salaam, whereas Allah, may He be glorified, has instructed us to
send both blessings and greeting of peace upon him, as He says
(interpretation of the meaning):

“Allah sends His Salat (Graces, Honours, Blessings, Mercy, etc.) on the
Prophet (Muhammad SAW) and also His angels too (ask Allah to bless and
forgive him). O you who believe! Send your Salat on (ask Allah to bless) him
(Muhammad SAW), and (you should) greet (salute) him with the Islamic way of
greeting (salutation i.e. As-Salamu Alaikum)”

[al-Ahzaab 33:56]. 

The scholars have stated that it is makrooh for a person to always mention
salaah (blessings) without salaam (greeting of peace), or to always mention
salaam without salaah. But if he mentions both of them, or mentions salaah
on its own sometimes, or salaam on its own sometimes, then he is fallowing
the verse. And Allah knows best.

See: Fath al-Baari, 11/167 

And Allah knows best.