One excellent approach is building the second date around previously discovered similarities.
If the two of you talked earlier about your mutual love of Indian food, science fiction and bowling, plan your second date around one or more of those interests.
This is the perfect opportunity to move your dating away from the dinner table or bar and into a weekend day out. It is still too early to offer dinner at your own apartment or theirs but you need more time now to get to know each other and the phone won't assist you.
You need human contact and interaction with your love-interest.
When you finally meet someone you connect with, that first date feels like magic.
The conversation flows smoothly, the chemistry is electric, and you wish that the night would never end.
Book shops, browsing, a market, antique stalls, a sport, a club, a shopping trip. But as you both feel you need to seek out some further intimacy a lunchtime meeting can extend throughout the afternoon and into evening, depending on how you feel about one another. A weekend afternoon lends itself to ebbs and flows, you can talk openly at a cafe table and then walk and feel how it is to walk next to your date.
If you told lies, you will have to be extremely careful about what you say. If we establish that you weren't creating a facade on the first date and were being yourself then the second date is to establish more of the same but on a grander scale with more detail.
For example, I accompany the Love King to craft beer tasting events, although that sort beverage does nothing to excite my tastebuds.
In return, he tags along on excursions to nurseries where I exclaim over new plants (which all look the same to him).
I therefore recommend you establish if possible a Saturday or Sunday lunchtime to meet so that you can combine a coffee or light lunch with a walk in the park or on the beach, maybe throw a ball about or go to a sporting occasion. A second date is too early for theater or movies because you must communicate a lot at this stage.
Therefore you need a place to walk and talk and start to feel comfortable in each others' company.