First Japanese...

The Japanese word for teacher is Sensei.  The founder of Aikido, Mr Ueshiba, is known as O Sensei or great teacher.  

On the mat, the instructor is referred to as Sensei.
 
Etiquette

At the beginning of class we bow to O Sensei, then bow to Sensei and say “o ne gai shi mas”, which means ‘please’ - in this context ‘please practice’.  At the end of class we bow to O Sensei, then bow to Sensei and say “domo arigato gozaimashita” which is a very polite ‘thank you’ (generally, the longer a phrase is the more polite it is).

When practising with a partner we bow to each other before and after training together.

Bowing in the dojo is used to show respect to the memory of the founder of Aikido, to the instructor and to fellow Aikidoka (practitioners of Aikido). It is not to be construed as an act of worship.

Tori    the person performing the technique
Uke   the person receiving the technique (usually the attacker)
 
Posture

Kamae    posture (general)
Hanmi    half body posture
Migi       right foot forward
Hidari     left foot forward
 
Tai Sabaki (body movement)

Irimi   entering body (step forward)
Tenkan    (pivot on the front foot)
Tsugi ashi      following feet (move the front foot forward, draw the rear foot up behind)
Ukemi  (receiving body) break falls
Mae       forwards
Ushiro       backwards
Yoko       sideways
Shikko   knee walking
 
Introduction to techniques

An Aikido technique is described by the attack, followed by the name of the technique.  Sometimes it is specified whether the technique should be sitting or standing.

Most techniques have two forms, omote (positive, irimi) and ura (negative, tenkan).  

When practising in pairs it is usual for one person to perform the technique four times (omote, right and left; ura, right and left), then the other person to perform the technique four times.
 
Suwariwaza   sitting techniques
Tachi waza standing techniques
Hanmi handachi sitting technique, standing attack
 
Attacks

Katatedori     wrist held by one hand
Aihanmi   (agreeing posture) right takes right or left takes left
Gyakuhanmi     right takes left or left takes right
Katadori      shoulder holding
Ryotedori  ryotemochi   both wrists held
Morotedori    one wrist held by two hands
Shomenuchi    vertical cut down
Yokomenuchi    diagonal cut down
Tsuki    punch
Jo dan      upper level (punch to face)
Chu dan      middle level (punch to the knot on the belt)
Ge dan      lower level (!)
Ushiro    behind
 
Techniques

Ikkyo first technique (circling arm)
Nikyo second technique (painful wrist twist)  
Sankyo   third technique (turning wrist and forearm)
Yonkyo   fourth technique (cutting forearm while applying pressure to a nerve)
Gokyo   fifth technique (applied to the wrist)
Rokkyo   sixth technique (applied to the elbow)
    
Iriminage   entering body throw
Ko te gae shi   little hand turn
Shi ho nage four direction throw
Kai ten nage body turn throw
Uchi    inside (under)
Soto     outside
 
Weapons

Jo  stick
Bokken  wooden sword
Tanto  wooden knife
 
Aikido Concepts

Tegatana  (hand blade) the edge of the arm from the base of the little finger to the forearm
Ki  energy
Tanden   centre, point below the navel which is the centre of ki
Kokyuho    breath power
Atemi  strike to distract ukei
Ma ai   distance, space or being in the right place at the right time
Zanshin    finishing, spirit at the end of the technique 
 Counting

Numbers are  regular, once you know one to ten you can go all the way to 99.  The exception is 4 which can be pronounced either shi (shi ho nage) or yon (yon kyo).

1  Ichi
2  Ni
3  San
4  Shi (or Yon)
5  Go
6  Rokkyu
7  Shichi
8  Hachi
9  Kyu
10  Ju