What To Practice In Training Mode

1) Combos

Every character has Bread and Butter (BnB) combos that need to be perfected. For you to be successful with your character of choice, you need to be able to perform these combos consistently in both familiar and unfamiliar situations. I like to practice each combo 30 times in a row. If I fail the combo, I start over at zero again. In addition, certain characters are much more dangerous when you can land specific combos. As an example, here are a few combos you need to be able to do with Abel before you can do serious damage with him:
- cr.HP xx HP Falling Sky
- Forward Kick xx dash, close HP xx HP Change of Direction
- cr.MK xx LP Change of Direction xx Focus cancel xx dash forward, cr.HP, Soulless

If you need help finding these combos for your character, the forums at shoryuken.com are a great place to start.

2) Punishes

Effective punishing skills will ensure that your damage output is maximized. A lot of moves in the game are unsafe; that is, if you block it, you can immediately counterattack and it will be guaranteed to land. Example: After blocking Cody's Zonk Knuckle (any strength), Abel can punish with Forward Kick (into combo). Go into training mode then set Cody to do Zonk Knuckles followed immediately by blocking. Practice landing that Forward Kick after blocking the Zonk, and no Cody will Zonk you ever again.

3) Hit-Confirming

Hit-confirming, if you didn't know, is the ability to turn a sequence of attacks into a combo on reaction. The simplest example is with Ken's cr.LK, cr.LP string. if this string is blocked, Ken is safe and can go for throw mixups, overheads, or defensive play. But if it hits, Ken can go into a HP Shoryuken. The basic skill here is seeing and recognizing that the two light attacks connected or were blocked. Some character types, like the Shotos, rely heavily on hit-confirming for their damage, so this is an essential skill.
To practice hit-confirming, simply set the dummy's guard to "random". In addition, you'll need a hit-confirmable combo to practice. As a rule of thumb, a combo is hit-confirmable if it consists of 3 or more attacks and is interruptible between each attack. It's also a good idea for the first two attacks to be safe on block. The easiest example is Ken's cr.LK, cr.LP, HP Shoryuken combo (link the Shoryuken). Another would be Chun Li's cr.LP, cr.LP, st.LP, st.HP combo.

4) Throw Teching

Teching throws is difficult for most beginners. The hard part is learning exactly when to press the buttons to tech the throw. If you press them too early, you stop blocking and are open to attack. Press them too late and you get thrown anyway. Set the dummy to do throws in a particular rhythm, such as the 4th beat of a 4/4 time measure in music. Practice teching the throw standing as well as crouching, taking note that the timing for the two different techs is slightly different. (A crouching tech must be slightly delayed)
As a side note, I'd like to mention that I've seen lots of intermediate players adapt a particular strategy for avoiding throws while blocking. They do a crouching tech after every normal they block, assuming that if the next attack is a throw it will be teched, and if it's another normal nothing will happen since I'm in blockstun. This is highly dangerous and you will have your face ROCKED at the next big tournament you go to. This only works against people who don't know how to delay their pokes to catch tech attempts. In other words, people who have boring and predictable offense.

5) Situational Training

Did you know that Juri can jump at a particular spot where her j.MK will cross you up but her j.HP will not and knock you down on your ass? Did you know that C.Viper can hop over your corpse with her Viper Elbow (F+MP) even in the corner? Most characters have tricky things like this that you'll need to know about before you can combat them effectively. You don't want random situations to happen at the end of a heated tournament match. Use training mode with lots of different characters and situations to see if you can find anything new that you might find useful. Barring that, after suffering a defeat because of one of these tactics, reproduce it in training mode to find its counter. Always remember, there is no uncounterable move or strategy.