Ancestor worship is a phrase which defines two different practices; the practice of worshiping one's ancestors as deities and the practice of honoring one's ancestors as progenitors. The second type is often lumped into the phrase, rather than being considered actual worship. The first kind is generally the least common in modern religions/practices, while the second form is fairly common within any sort of reconstructional groups. Taoist beliefs include deified ancestors being worshiped and prayed to, as do a few other Eastern religions, whereas most Western belief systems will regard decreased ancestors as blessed dead. However, there are some practices which contain both, such as Kemeticism which balances some deified ancestors (Imhotep, etc) with blessed dead whom are cared for by the living.
There are several reasons to begin ancestor worship, and little reason not to.
Ancestor worship gives a connection to the past, to the ones who've come before. Many people today are completely unconnected to their past, their families, or their origins. For many this leaves them in a state of disconnection, feeling lost. For many new pagans, witches, etc, this is either a point of no thought or one that they feel is pointless (as many families are Christian), but it is also why so many start out as eclectic; they simply have no foundation. Ancestor worship gives a person that foundation.
Ancestor worship brings different blessed dead and/or deified dead into your spiritual corner. While working with deities is very spiritually helpful, having a deceased relative who knows what it is to be human, to feel the things we do, to do the things we do, is a different sort of helpful. Explaining car trouble to a deity is that much harder than explaining it to Grandpa Smith and asking for help. Or explaining lady problems to Grandma Jane as opposed to male gods.
Ancestor worship can be practiced by anyone, whether they know or like their direct ancestors or not. There are many levels to ancestor worship; family/friend, community, national, and international. You do not need to be related to someone to celebrate their life and the good that they've done. (For instance I honor Robin Williams as blessed dead.)
On the family/friend level one can also honor spiritual family, past lives, adoptive family, foster family, etc; generally this category is for anyone whom you've known in life or are directly related to. This can go back only a few generations then become widespread (unknown blessed/deified dead), or it can be incredibly specific for some. This category can include or discredit individuals based on various factors ranging from behavior in life to wishes in death to how they are being worshiped/honored. Some will refuse any interactions in this manner while others will be more than happy to have an active afterlife. This is the same for the other levels of ancestor worship.
On the community level it is much the same, but in regards to people within your community; for instance, I include some of my passed coworkers within my ancestor worship. I do this because of the beautiful people they are, and the good things that they did; their strengths bring me pride for knowing them. Similarly, this can be done within any community.
On the national level you have national heroes whom reap some form of ancestor worship due to to their particular status. This is where people like FDR, Robin Williams, etc, would stand for the US and people like Guy Fawkes, Martin Luther, etc, would stand for the UK. (These are just examples please refer to your particular country's heroes.) Even people you never met, nor know all about can be honored/worshiped at this level.
The international level involves worshiping/honoring those beyond your particular country. In my case, I honor all the known and unknown dead from my belief system. Some of their names are remembered and honored at particular times, while others are not honored in this particular way.
It is rather easy to begin an ancestor worship practice and does not have to be elaborate or zany or decorative in the same way a deity based practice might be.
All you really need to start is a space in which to keep/set up a shrine/altar to the blessed/deified dead you are looking to honor/worship. This can be a table, a cabinet shelf, a box. On/inside this you place a candle/light, some form of scent, a container for water/liquid offerings, and a container for food/solid offerings. The food and water that are being offered do not need to be large in quantity; they are actually better to only give small quantities of as it is not recommended to ingest offerings to the dead. You will also need images/representations of the individuals you are wishing to include in this. Ensure that these images/representations do not include the images/names of living people, as again it is not something recommended. You can also add in various items that your dead liked/would've liked in life.
The reason why ingesting offerings and having the images/names of living people included in ones ancestor worship is that the association between dead and living can become as great as to place a sort of curse upon the living. The living person will become too associated with the dead and death that they may soon follow suit.
It can be something small enough to be slid under a bed, but also as big as an outdoor altar space. It really depends on the practitioner and what they (and their dead) desire.