(1) Resistance e.g. adding more weight.
(2) Number of repetitions with a particular weight. 
(3) Number of sets of the exercise.
(4) Intensity, i.e. reducing the recovery periods. 

Which weight training exercises?
The exercise must be specific to the type of strength required, and is therefore related to the particular demands of the event or aim of the individual (specificity). 

Design your routine to work your larger muscle groups first, such as your chest and back, prior to working the smaller muscles like the biceps and triceps.

This aids in warming up your smaller muscles, and allowing you to lift heavier weights, simply because your smaller muscles aid in both the lift, and keeping correct technique. 

How many, how much?
For maximum strength the loading should be high (85-100%) of 1 rep max, (the maximum load that you can lift) and the repetitions few (1-5). 

The number of sets used will reflect the number of repetitions used (e.g. 6-8 sets of single repetitions is within reach, but to perform eight sets using five repetitions is physically very difficult to do). 

Elastic Strength is obtained by working with moderate poundage's (65/80%) 
Permitting faster movement with 8-12 repetitions, 3 sets are adequate for substantial gains. 

Strength Endurance is achieved by repeating exercises for the highest possible number of repetitions in total, with resistance's representing 40% to 60% of maximum recommended, (Circuit training is a suitable activities). 

Handling heavy weights in the pursuit of strength will require a recovery of 2-3 minutes between sets, but only minimum recovery should be taken if strength endurance is the aim, 30 60 seconds.

Avoid allowing your muscles a chance to cool down, however give them enough rest before you start your next set. 

How often?
This is really linked with recovery since the body must be allowed to recover from the strenuous demands of strength training. As a 'rule of thumb' 48 hours should elapse between sessions, avoid training sore muscles.

If training strenuously, you will find it extremely difficult to maintain the same level of lifting at each session, and the total poundage lifted in each session would be better to be varied (e.g. a high, low and medium volume session) each week.

Remember muscles don't grow in the gym, they grow through proper rest and nutrition. 

What sort of weight lifting equipment?
There are variable resistance machines and free weights. 

Variable resistance machines are effective tools for building strength and muscle tone and are designed to work the target muscle in isolation, without the assistance of the surrounding muscles. 

Free weights barbells, dumbbells allow you not only to target a particular muscle group but also to engage other muscles that assist in the work. 

Lifting free weights improves your co-ordination by improving the neuromuscular pathways that connect your muscles to the central nervous system. 

Training Systems

Simple Sets:
3 x 8/12 with 70%--meaning three sets of 8/12 repetitions with a weight of 65% of maximum for one repetition. 

This is the system that all novice lifters should work on, because the high number of repetitions enables the lifter to learn correct technique, and thereby reduce the risk of injury. 

Pyramid System 
Here the load is increased and the repetitions are reduced (e.g. 100kg x10, 120kg x 5, 130kg x 4, 140kg x 3, 150kg x 2, 160kg x 1). Pyramid lifting is only for experienced lifters who have an established good technique. 
 

The following are methods of high intensity training, and should be done by individuals with a good lifting background.  These should be used sparingly to shock the muscles or to help you get over a plateau.  Allow for adequate warm-up and rest and go to positive failure on each set.

Forced Reps: After positive failure is reached spotters assist  you in doing a couple of more reps.