Step 1: Import the .ai file
Open the file with File > Open... (Ctrl+O) at app.svgsketch.com, or drop it onto the canvas. Select the artboards you need in the dialog and click "Import". Each artboard becomes a view; a single artboard is simply the document.
Step 2: Decide what happens to text
Leave "Keep text editable" selected when the SVG will be edited later or must stay accessible as text. Choose "Convert text to outlines" when the SVG must render identically everywhere without the fonts installed. Either way the report lists the fonts involved.
Step 3: Check the report
Open File > Last Import Report.... Effects, brushes and meshes arrive flattened from the PDF rendition and are listed as approximated or rasterized; spot colors are listed by name after conversion to sRGB. Anything dropped is named so you can decide whether it matters.
Step 4: Export SVG
In the Export panel choose SVG and enable "Optimize with SVGO". Layer and object names become ids and titles in the SVG, so the structure survives into other tools. The Illustrator import page covers what else carries over, and opening AI files without Illustrator covers editing them in place.
Batches: use the command line
The @svgsketch/cli package converts without a browser: svgsketch convert design.ai -o design.svg writes SVG, svgsketch import design.ai -o design.svgs writes the editable document, and the --artboards, --text, --hidden-layers, --report and --fail-on-warnings options mirror the dialog. The same commands accept .eps and .pdf.