فرشاية السنان ومعجون السنان بالحمام جنب الصابون.

Because Arabic usually omits the present-tense to be in sentences like this.

So:

• فرشاية السنان ومعجون السنان بالحمام
  literally: the toothbrush and the toothpaste in the bathroom
• natural meaning: The toothbrush and toothpaste are in the bathroom

This is very normal in both Levantine and Standard Arabic. If you wanted past or future, then a form of كان might appear.

This is a possession-style structure, basically:

• فرشاية = brush
• السنان = the teeth

So فرشاية السنان is literally the brush of the teeth, which English expresses as toothbrush.

The same pattern appears in:

• معجون السنان = toothpaste
  literally paste of the teeth

This kind of structure is extremely common in Arabic.

Because السنان is the colloquial Levantine form, while الأسنان is the Standard Arabic form.

So:

• السنان = Levantine dialect
• الأسنان = Modern Standard Arabic

A native Levantine speaker would naturally say فرشاية السنان and معجون السنان in everyday speech.

بالحمام is made of:

• بـ = in / at
• الحمام = the bathroom

So بالحمام means in the bathroom or at the bathroom, depending on context.
Here, in the bathroom is the natural translation.

In Levantine, الحمام very commonly means the bathroom.

جنب means next to, beside, or by.

So:

• جنب الصابون = next to the soap

Arabic does not need an extra word like English to here.
It is simply:

• جنب
  • noun
• next to
  • noun

الصابون means the soap, not just soap in a general sense.

In this sentence, the speaker is probably talking about a specific soap in the bathroom, so the definite form is natural:

• صابون = soap
• الصابون = the soap

English sometimes says next to the soap in exactly the same way.

A more Modern Standard Arabic version would be:

• فرشاة الأسنان ومعجون الأسنان في الحمام بجانب الصابون

Main differences:

• فرشاية → فرشاة
• السنان → الأسنان
• بـالحمام → في الحمام
• جنب → بجانب

The Levantine sentence is more natural for everyday speech.

A rough pronunciation would be:

furshaayet is-snen w maʿjūn is-snen bil-hammām janb is-sābūn

A few notes:

• فرشاية often sounds like furshaaye / فرشاية
• السنان is often pronounced more like snen
• و here sounds like w = and
• بالحمام is bil-hammām
• جنب is janb

Exact pronunciation varies a bit by country and city, but this is a good general Levantine guide.