Hello Juliana,

So, first off, I suggest that you install and use the Engage Child theme (but I understand that you already have that ready?). It's the "engage-child.zip" file that is included in the theme's main package. Just upload it as a regular theme and activate it. After you do so, you can apply new CSS via Appearance / Theme Editor, without changing the parent theme's code. 

That custom CSS would be:

@font-face {    
    font-family: "MyFontName";    
    src: url(http://www.example.org/mycustomfont.ttf) format("truetype");
}
body, p {     
    font-family: "MyFontName", sans-serif !important;
}
h1,h2,h3,h4,h5,h6 {    
    font-family: "MyFontName", sans-serif !important;
}

If you want the font to apply to regular text only, then remove the "h1,h2,h3..." part. If you want the new font to be applied to headings only, remove the "body..". You may also use two different font files:

@font-face {    
    font-family: "MyFontName";    src: url(http://www.example.org/mycustomfont.ttf) format("truetype");
}
@font-face {    
    font-family: "MyFontNameBold";    src: url(http://www.example.org/mycustomfont_bold.ttf) format("truetype");
}
body, p {     
    font-family: "MyFontName", sans-serif !important;
}
h1,h2,h3,h4,h5,h6 {    
    font-family: "MyFontNameBold", sans-serif !important;
}

There are unlimited variations. Of course, you need to have your font files hosted somewhere. If the file is not ttf (TrueType which is of the highest quality), then you may use WOFF, like:

@font-face {    
    font-family: "MyFontName";    src: url(sansation_light.woff);
}

You may also try other font file formats but make sure they're compatible with modern browsers.