
To create the slide text effect in Premiere Pro you will need to have the text in .png format (for the learning purpose you can use mine below, or create your own for example in Adobe Photoshop, or by using different software).
Text is white with transparent background:

text-1

text-2
Follow the steps below and watch the video tutorial:
Step1.
Create a new sequence
Open Adobe Premiere Pro and create a new sequence:

In sequence settings set the frame size:

Step2.
Import a video (optional)
Import a video and drag it into the sequence. Got to Effect Controls to fit the video into a frame (scale, position):

Step3.
Import your text
Import your text and drag it into the sequence:

Step4.
Create a slide effect
Click on the first text and go to the Effects panel and type in the search bar – crop:

Drag the Crop option into the Effect Controls panel:

Crop your text from the top and bottom:

Go to the Effects panel and type in the search bar – transform (distort):

Drag the Transform option into the Effect Controls panel above the Crop option.
In the Transform option go to Position and add the first stopwatch. Click on the stopwatch and change the vertical position of the text (move the text down):

You can notice that the first text disappeared (went down outside the cropped area):

Move the blue line to the right (0.2-0.5 second) and add the second watch stop:

You can play your video to see the effect. To make the slide effect more smooth select both stopwatches and right-click, go to Temporal Interpolation and choose the Ease In or Ease Out option.

Click on the second text and repeat the steps from the first text (Crop, and Transform):

You can move the first stopwatch and the second stopwatch to the right to make a delay in appearing of the text (the second text will appear after the first text):

You can play your video to see the effect:

Watch also the video tutorial:
Read also:
How to create a GIF in Adobe Premiere Pro?