I've broken the reading process down into a few steps, mostly because that's how I think of it. Please share your own strategies in comments!
1. Your Spiel
No matter who I'm reading for, or how many times I have read for them in the past, I always start a reading off with my spiel. I keep it light-hearted, and I'm usually shuffling while I speak. It's important to let the querent know what they can expect from the reading, and what they SHOULDN'T expect. I recommend that your spiel include the limitations of tarot readings, as well as some description about the process. Here's a rough version of my spiel:
As you know, tarot is for entertainment purposes. It does not predict your future or read minds, but gives you a tool for looking at a problem from a new perspective. As I lay the cards out, I'll describe what each position means before turning the cards over and interpreting their meanings. You'll also have a chance to ask questions and bring your own interpretation to the table!
2. The Querent
In order for the querent to have a meaningful experience, you want them to be involved beyond just sitting there receiving the reading from you. Some people do this by asking the querent to shuffle the cards for them; I don't use this route. Not everybody knows how to shuffle, and even for people that do, tarot cards are usually a different size than traditional playing cards. This can make it difficult for querents to shuffle the whole deck.
I usually ask the querent to cut the deck, but even this can be confusing for people not familiar with card lingo. My favorite way of involving the querent is to give them a chance to hold the deck after I shuffle, and I tell them to "infuse the cards with [their] mojo." I say it a little tongue-and-cheek, and querents usually laugh or smile, but almost everybody instinctively knows what to do (which varies from querent to querent).
If you already know how to shuffle, then you are off to a good start. You'll have to practice with your deck, because tarot cards vary in size from deck to deck. I personally always do a riffle and bridge, but there are many ways to shuffle cards.
My only caveat for shuffling is that you may want to preserve the orientation of your cards. In traditional playing cards, it doesn't matter if cards get turned upside down. If, like me, you don't read tarot reversals, you will want to keep your cards oriented upright (one of my favorite tarot bloggers talks about reversals). This means taking the time between shuffles to make sure the halves of the deck are facing the same way. Alternately, you can just let the cards fall as they may, and just turn the reversed cards around when you do the reading!
There is some interesting conversation about how many times you need to shuffle a tarot deck to randomize it; I usually shuffle 10-12 times.
4. Laying out the Cards
I know some tarot readers lay their cards out already facing upward, to force them to read the card meanings more spontaneously and intuitively. I prefer laying them out one at a time, explaining to the querent what each position represents. Let's take a look at this three card spread, Mind-Body-Spirit; as I lay each card out, I would have said to the querent, "This card represents how your mind is addressing the issue. This card represents how your body is manifesting your concerns," etcetera etcetera. Before I even begin interpreting the cards, the querent would see their spread laid out as pictured to the right.
When I turn the cards over, I explain each card individually. Some tarot readers turn all the cards over before interpreting them, because each card can influence how you read other cards. I do the one-at-a-time approach for several reasons. First of all, it gives me time to be thoughtful about my interpretations. Secondly, I think it is less overwhelming for the querent. Finally, in my experience, the discovery of how the card meanings interact is more exciting if you turn the cards over one by one!
Here's the same reading, but half way finished: at this point, I'll have already discussed how the King of Wands describes the querent's mental state, and I'll be explaining how the Page of Cups might give insight into how the querent's body is dealing with the issue at hand. I haven't yet discussed the spirit, represented by the third (and still hidden) card.
When I finally have a spread finished, I will try to summarize the main themes of the entire spread; this is less important with small spreads like the one in this example, but for more complicated spreads like a Celtic Cross, it can be helpful for the querent.
It's also important for me to get some feedback from the querent without putting them on the spot. Since I don't ask for querents to share their question with me at the beginning, I will usually say something like, "Does this reading make sense?" or "Is this consistent with your question?" If they say no, I offer to hear their question and then re-interpret the cards based on what they've told me. Since each card has a variety of meanings based on archetype, you can usually find something meaningful (yes, I know it's the Barnum effect; remember, tarot isn't about divining some unique fate, it's about touching base with the universal human experience in order to help us organize our own reality).
When I started doing tarot, I found a lot of advice on what you "should" and "shouldn't" do for readings, often based on spiritual or supernatural beliefs. These guidelines often produce a rich experience for folks, but chafe a little for me personally. I've shared with you my specific approach, but if I had to leave you with a few simple pointers, they would be:
1. Be upfront with the querent about what tarot is; don't promise to solve problems or provide predictions of the future/insight into third party motivations.
2. Create some small form of ritual around your readings. Whether it's your speil, the way you shuffle, or how you address the querent, humans respond to ritual. It will also give you confidence for readings.
3. Have fun and do what feels natural! Which, frankly, is pretty good advice for life in general.