To do this, you will need to add some custom CSS into your CSS file.
Okay, let's take a sample.
Here's our first form: Original Form
Now, let say we want to have Phone field sit next to Email field, like this one: Final Form
What we need to do is look in the HTML code and find the
<li> elements surrounding those fields (Phone and Email).
Inside that element is an id value. For example Email might have li_2 and the Phone field would have li_3.
With those id values, you can use the following CSS to target and float the fields next to each other:
#li_4 is the next element after the aligned fields. We need to add this to reset the alignment.
Copy that code into your CSS file and save it. (Click Edit CSS from your Admin panel)
Refresh your form and those fields should have the new alignment.
I realized this is quite some work, so if you need any help, just post it here and I'll try to help.