You have several possibilities:
The sensor device sends data directly to the mobile phone using BLE (Bluetooth Low Energy). This usually requires a dedicated app on the phone, but no special setup, the app can scan for devices matching yours, connect, retrieve data and so on automatically. You’ll probably want a way to “authenticate” so that only the rightful owner can talk to the device (either some kind of pairing code, or a button to activate a pairing period...).
The sensor creates a Wi-Fi network, and the smartphone connects to it. No app needed, but the user must connect to that network, and of course won’t have Internet access while connected. This is usually only useful for a short period of time during configuration of the device. You can simplify the “connect to the network” part using a QR code or NFC tag or an app.
The sensor connects to the existing WiFi network, and then either the phone and sensor can “talk” to each other directly (though this is most likely to be quite power-hungry, as the sensor would need to remain connected and active nearly all the time), or both talk to a remote (cloud) server: the sensor sends data to the server (and receives configuration if needed), the phone receives status and data from the server.
To simplify the connection process you probably want a prior communication via another channel (BLE is a good option) so that the phone can send the WiFi config to the sensor.
The sensor talks to a gateway over BLE or Zigbee or some other protocol of you choice, and the phone either talks to that gateway or they both talk to a remote server like in the scenario above.
There are probably quite a few others, as well as combinations. Which one is best really depends on your exact scenario, in terms of how much data, how often, whether your are running in battery or not, what battery life you need, whether you need remote access, etc.
If you need WiFi the ubiquitous solutions are ESP8266 or ESP32 based boards. For BLE, ESP32 or nRF5 (e.g. nRF52832) or quite a few others. For Zigbee, nRF52840 and quite a few others.
The biggest concern is usually the battery. To remain small, you need to lower power consumption a lot, and that often rules out WiFi unless you really transmit very seldom (e.g. once a day). BLE and Zigbee are more suitable for long battery life.