Hi,
Do your best is either 最善(さいぜん)を尽(つ)くす (Saizen wo tukusu) 。or ベストを尽(つ)くす (Besuto wo tukusu)。
It sounds a bit strange/funny to say both "today" and "always" in a sentence in Japanese so I'd suggest the following:
今日から最善をつくしてください。kyoukara saizen wo tukushitekudasai. (From today on, do your best).
常にベストを尽くしてください。Tsuneni besuto wo tukushite kudasai. Always do your best.
いつもベストを尽くしてください。Itsumo besuto wo tukushite kudasai. Always do your best.
Less polite form by men: change "尽くしてください” "Tukushite kudasai" to "”尽くせ” tsukuse.
Less polite form by women: change "尽くしてください” "Tukushite kudasai" to "尽くしてね” tsukushitene.
I hope this helps.