Yeast comes from the store in a tube, slap pack, or in the case of dried yeast, a packet much like bread yeast. Even with the date on the container, there is no guarantee that the yeast has not been mistreated at some point after leaving its place of origin. Doing a mini brew using a pint or so of water with some malt extract and hops and adding yeast to this cooled medium a couple of days prior to brew day is an excellent way to assure an active healthy yeast strain is being added to a batch of beer. I use a brewpub growler with a piece of aluminium foil over the top (aluminium foil does not attract baddies and is sanitary). Soak the growler in chlorinated water along with a funnel. Boil a quarter to half cup of malt extract with a few hop pellets for about 15 minutes or so, then cool it to room temperature in a water or ice water bath. The yeast may be added once cool and the chilled wort has been poured into the growler (rinse the funnel and growler with hot water first). Follow the instructions for the yeast and treat the yeast as if it is being added to a full batch. On many occasions I have had issues with the yeast starter and getting no activity by brew time. From my experience, it is better to either postpone brewing to wait until the yeast starts or start again with fresh yeast from the store. If the yeast starts late, more wort may be added to keep it active until brew day. I have gotten coupons from White Labs for bad yeast in the past. Wyeast slap packs are a good alternative, as the yeast comes with their own wort starter in the pack. The pack will inflate, showing that the yeast is active and fine. A starter would be necessary still for higher gravity brews.
It is a general rule of thumb that liquid yeasts will produce higher quality brews, and there are more varieties of liquid yeast available to the brewer. Dried yeast does contain contaminants, wild yeast, that is, but is of better quality than it used to be. Liquid yeast is pure yeast harvested from a single cell.Experiment with various strains and compare with dry strains to see what the differences in beer quality are.
In the case of lagers, getting the yeast as active as possible is crucial for obtaining a quick start. Stepping the yeast up more than once can he helpful here giving the yeast population the opportunity to grow. Same applies in the case of higher gravity brews. The White Labs labels actually say that a starter should be made for gravities over 1.07.
A key to a successful brew is to match the wort temperature with the temperature of the starter as best as possible. This avoids a yeast shock, and helps with a quick start.
Another thing that can be done to improve a batch of beer is to pour off the fermented liquid in the starter vessel leaving just enough liquid to make the yeast slurry on the bottom pourable. The fermented "beer" has concentrated fermentation byproducts in it and is not needed in for the beer that can add off flavors to the finished product.
Liquid yeasts can be harvested or re-used from the bottom of the fermentor. I have had success re-using ale yeasts as many as six times, and lager strains as many as four. I have read that dry yeasts should not be re-used as the yeast tends to mutate more readily into something that is not desireable. I usually pour the yeast slurry at the bottom of a freshly transferred batch right into a freshly created wort.