There are three nouns and five verbs translated worship in the Greek New Testament. Mr. W. E. Vine sums up the conclusion to "worship," "…broadly it ("worship," dm) may be regarded as the direct acknowledgment to God, of His nature, attributes, ways and claims, whether by the outgoing of the heart in praise and thanksgiving or by deed done in such acknowledgment" (Expository dictionary of New Testament Words).
Now that you have a definition of what Worship really means, we can start there!
1. Expression of approval, commendation, or admiration.
2. The extolling or exaltation of a deity, ruler, or hero.
3. Archaic A reason for praise; merit.
Thanksgiving \Thanks"giv`ing\, n.
1. The act of rending thanks, or expressing gratitude for favors or mercies.
Every creature of God is good, and nothing to be refused, if it be received with thanksgiving. --1 Tim. iv. 4.
In the thanksgiving before meat. --Shak.
And taught by thee the Church prolongs Her hymns of high thanksgiving still. --Keble.
2. A public acknowledgment or celebration of divine goodness; also, a day set apart for religious services, specially to acknowledge the goodness of God, either in any remarkable deliverance from calamities or danger, or in the ordinary dispensation of his bounties.
1. That which is done or effected by a responsible agent; an act; an action; a thing done; -- a word of extensive application, including, whatever is done, good or bad, great or small.
And Joseph said to them, What deed is this which ye have done? --Gen. xliv. 15.
We receive the due reward of our deeds. --Luke xxiii. 41.
Now that those components are defined we can go forward!
Ok so what we have by breaking it down by definition is a functional "map" to follow!
Your family can choose to Worship together by Praising God/Jesus through Prayer, Song or even Talking about how much you admire and exalt Him!
You can Worship together by in Thanksgiving in Prayer, Song, or Talking about how much you appreciate all God/Jesus has done for you. Discuss particular answers to prayer. Times you have avoided danger and you felt His presence!
Your family can Worship together in Deed, by service within the Church or Community, by spreading the Word, By avoiding Sin!
I pray this has helped you!