Ember days - from the Latin "QuattuorTempora" meaning "Four Seasons" - are traditional days of fasting and almsgiving for Western Christians.
The Four Embertides coincide with changes in the seasons and have been used by farmers to determine planting and harvesting times. Ember days fall on the Wednesday, Friday, and Saturday of the prescribed week:

Winter: St. Lucy Day (December 13) 
Spring: Invocabit, The first Sunday in Lent
Summer:  Pentecost
Fall: Holy Cross Day (September 14)

A Lutheran suggestion to the practice of fasting can be found here 
These readings are meant to be part of the Divine Service, but of themselves serve as a good addition to fasting and almsgiving on Ember Days.
 

The Fourth Lesson

Zechariah 8:14-19

“For thus says the Lord of hosts:

‘Just as I determined to punish you
When your fathers provoked Me to wrath,’
Says the Lord of hosts,
‘And I would not relent,
So again in these days
I am determined to do good
To Jerusalem and to the house of Judah.
Do not fear.
These are the things you shall do:
Speak each man the truth to his neighbor;
Give judgment in your gates for truth, justice, and peace;
Let none of you think evil in your heart against your neighbor;
And do not love a false oath.
For all these are things that I hate,’
Says the Lord.”
Then the word of the Lord of hosts came to me, saying, “Thus says the Lord of hosts:

‘The fast of the fourth month,
The fast of the fifth,
The fast of the seventh,
And the fast of the tenth,
Shall be joy and gladness and cheerful feasts
For the house of Judah.
Therefore love truth and peace.’

The Verse: Let my prayer be counted as incense be- | fore you,*
and the lifting up of my hands as the evening | sacrifice!

The Fifth Collect: O Lord, as Thou does grant us this wholesome fast: so also grant us, we beseech Thee, the help of Thy pardon; through Jesus Christ, Thy Son, our Lord, who liveth and reigneth with Thee and the Holy Ghost: ever one God, world without end. Amen.

The Fifth Lesson

Daniel 3: 52-56 (Song of the Three Children 26-28)

 In those days: The Angel of the Lord came down into the oven together with Azarias and his fellows, and smote the flame of the fire out of the oven; and made the midst of the furnace as it had been a moist whistling wind, so that the fire touched them not at all, neither hurt nor troubled them. Then the three, as out of one mouth, praised, glorified, and blessed, God in the furnace, saying:   

Hymn: Bendictus es, Domine

Bless-ed art thou, O Lord Gód of our fáthers: * and to be praised and exalted above áll for éver. 
And bless-ed is Thy glórious and hóly name: * and to be praised and exalted above áll for éver. 
Bless-ed art Thou in the temple of Thine hóly glóry: * and to be praised and exalted above áll for éver.
Bless-ed art Thou that beholdest the depths, † and sittest upón the chérubim: * and to be praised and exalted above áll for éver. 
Bless-ed art Thou on the glorious thróne of Thy kíngdom: * and to be praised and exalted above áll for  éver. 
Bless-ed art Thou in the firmamént of héaven: * and above all to be praised and glorifíed for éver. 
O give thanks unto the Lord, because Hé is grácious: * for His mercy endúreth for éver. 
Glory be to the Fáther and tó the Son * and tó the Hóly Ghost. As it was in the beginning, is now, and éver sháll be, * wórld without énd. Amen

The Sixth Collect: O God, who for the deliverance of the three children didst assuage the flames of fire: mercifully grant that the fiery assaults of temptation may have no power upon us Thy servants; through the same Jesus Christ, Thy Son, our Lord; who liveth and reigneth with Thee and the Holy Ghost: ever one God, world without end. Amen.

The Epistle

Hebrews 9:2-12

For a tabernacle was prepared: the first part, in which was the lampstand, the table, and the showbread, which is called the sanctuary; and behind the second veil, the part of the tabernacle which is called the Holiest of All, which had the golden censer and the ark of the covenant overlaid on all sides with gold, in which were the golden pot that had the manna, Aaron’s rod that budded, and the tablets of the covenant; and above it were the cherubim of glory overshadowing the mercy seat. Of these things we cannot now speak in detail.

Now when these things had been thus prepared, the priests always went into the first part of the tabernacle, performing the services. But into the second part the high priest went alone once a year, not without blood, which he offered for himself and for the people’s sins committed in ignorance; the Holy Spirit indicating this, that the way into the Holiest of All was not yet made manifest while the first tabernacle was still standing. It was symbolic for the present time in which both gifts and sacrifices are offered which cannot make him who performed the service perfect in regard to the conscience— concerned only with foods and drinks, various washings, and fleshly ordinances imposed until the time of reformation.

But Christ came as High Priest of the good things to come, with the greater and more perfect tabernacle not made with hands, that is, not of this creation. Not with the blood of goats and calves, but with His own blood He entered the Most Holy Place once for all, having obtained eternal redemption.

The Holy Gospel

Luke 13:6-17

Praise the LORD, all | nations!*
Extol him, all | peoples!
For great is his steadfast | love toward us,*
and the faithfulness of the LORD endures forever. |
Praise the LORD!

He also spoke this parable: “A certain man had a fig tree planted in his vineyard, and he came seeking fruit on it and found none. Then he said to the keeper of his vineyard, ‘Look, for three years I have come seeking fruit on this fig tree and find none. Cut it down; why does it use up the ground?’ But he answered and said to him, ‘Sir, let it alone this year also, until I dig around it and fertilize it. And if it bears fruit, well. But if not, after that you can cut it down.’”

Now He was teaching in one of the synagogues on the Sabbath. And behold, there was a woman who had a spirit of infirmity eighteen years, and was bent over and could in no way raise herself up. But when Jesus saw her, He called her to Him and said to her, “Woman, you are loosed from your infirmity.” And He laid His hands on her, and immediately she was made straight, and glorified God.

But the ruler of the synagogue answered with indignation, because Jesus had healed on the Sabbath; and he said to the crowd, “There are six days on which men ought to work; therefore come and be healed on them, and not on the Sabbath day.”

The Lord then answered him and said, “Hypocrite! Does not each one of you on the Sabbath loose his ox or donkey from the stall, and lead it away to water it? So ought not this woman, being a daughter of Abraham, whom Satan has bound—think of it—for eighteen years, be loosed from this bond on the Sabbath?” And when He said these things, all His adversaries were put to shame; and all the multitude rejoiced for all the glorious things that were done by Him.