How often you workout each week depends on whether you are looking for strength gains or hypertrophy gains (muscle growth).
Strength gains are simple – you want to work out as often as you can recover from, whilst staying away from hitting failure during your sets. 5 days per week whilst cycling your weights (as discussed in this article) is a great setup, although 3 days per week will also work, just expect slower strength gains.
Hypertrophy workouts are a little more complicated, but can be summed up by saying the volume needs to increase as the experience of the athlete increases:
Beginners
Someone who has never lifted a weight before could progress with only 1 workout per week, but that will only take them so far. One major drawback to training once a week is that you will always experience DOMS (muscle soreness) after a workout. Working out more frequently cuts this out.
Ideally a beginner would start with 2-3 full body workouts per week with minimum volume. This would allow for practise of the lifts whilst also keeping DOMS low. An even better solution for the beginner would be starting off with a strength building routine to get them up to a base level so they can assess what they are really starting with. How can someone who has never lifted a weight know what parts of their bodies they need to work? It’s much better to get reasonably strong first then see what muscle you have built.
Intermediates
Intermediates would do better with an upper/lower split 3-4 times per week. This allows for more volume to be added to each muscle group each workout. This causes more damage to the muscle but recovery time between the same workouts goes up due to the upper/lower split. Eg you work upper one day, lower the next, day off, upper, lower, 2 days off.
Advanced
Not many people will reach this stage, but this is where volume should get a bit crazy. 3 way splits over 6 days a week wouldn’t be out of place here. Note that this is where a lot of the super high volume & frequency muscle magazine routines come from. It’s just a shame they don’t admit that they are more suited to advanced bodybuilders, rather than the beginners they aim the magazines at.