One thing I love to teach people as a Hellenic priest and writer is how to construct places of worship and carry out rites. One of the reasons I enjoy teaching this is because it's not as hard or costly as some people might think or portray, especially if you're creating what I call "natural altars." It is not a complicated trade whatsoever. Lots of practitioners have really beautiful and elaborate shrines and altars with numerous statues and the like, but these things are not needed to carry out Hellenic worship. All you really need is a basic altar where you can pray, make offerings and sacrifices, and carry out ritual work. The fancy things are nice, and can indeed help with focus, but it's important to remember that the niceties are not what you're worshiping. The Gods, Spirits and Heroes are not statues, temples, or elaborate tapestries and pottery. To connect with the Gods simply because they are the Gods, is the greatest achievement.
As you can see in the picture above, the main altar of my own shrine is a simple stack of stones, which is a traditional structure of the Greek altar. It's a very simple design. These earthly pebbles were purchased for less than $1, but you can also find natural stones probably out in your yard or driveway. You only need to properly wash and cleanse them before making into an altar. Upon this stack of simple natural stones, once dedicated to your worship and the Gods, you can carry out any kind of religious practice that needs or involves an altar or a worship space. Incense can be burned upon it, libations poured, and general offerings placed. It's also very appropriate to recite prayers, hymns and practice worship here.
So if you want to make a genuine Hellenic altar right now, find yourself a proper and safe surface, go get some natural stones, and cleanse and stack them there. This simple, virtually cost-free method is all you need to begin practicing Greek Polytheism. Everything else can come later in good time as you are able, should you choose.
To dedicate and officially "open" your natural altar, you might recite a prayer along these lines and light a cone of incense as your first offering to The Dodekatheon at this structure,
Upon this sacred structure,
I request the blessings and recognition of the Gods of Olympus,
that it may now be a holy altar in their honor and glory.
In the Goodness of the Gods,